diff --git a/clippy_lints/src/operators/arithmetic_side_effects.rs b/clippy_lints/src/operators/arithmetic_side_effects.rs
index 929efb6c574d5..96ea063aa74d6 100644
--- a/clippy_lints/src/operators/arithmetic_side_effects.rs
+++ b/clippy_lints/src/operators/arithmetic_side_effects.rs
@@ -1,11 +1,11 @@
 use super::ARITHMETIC_SIDE_EFFECTS;
 use clippy_utils::consts::{constant, constant_simple, Constant};
 use clippy_utils::diagnostics::span_lint;
-use clippy_utils::ty::type_diagnostic_name;
+use clippy_utils::ty::is_type_diagnostic_item;
 use clippy_utils::{expr_or_init, is_from_proc_macro, is_lint_allowed, peel_hir_expr_refs, peel_hir_expr_unary};
 use rustc_data_structures::fx::{FxHashMap, FxHashSet};
 use rustc_lint::{LateContext, LateLintPass};
-use rustc_middle::ty::Ty;
+use rustc_middle::ty::{self, Ty};
 use rustc_session::impl_lint_pass;
 use rustc_span::source_map::Spanned;
 use rustc_span::symbol::sym;
@@ -88,37 +88,44 @@ impl ArithmeticSideEffects {
     }
 
     /// Verifies built-in types that have specific allowed operations
-    fn has_specific_allowed_type_and_operation(
-        cx: &LateContext<'_>,
-        lhs_ty: Ty<'_>,
+    fn has_specific_allowed_type_and_operation<'tcx>(
+        cx: &LateContext<'tcx>,
+        lhs_ty: Ty<'tcx>,
         op: &Spanned<hir::BinOpKind>,
-        rhs_ty: Ty<'_>,
+        rhs_ty: Ty<'tcx>,
     ) -> bool {
         let is_div_or_rem = matches!(op.node, hir::BinOpKind::Div | hir::BinOpKind::Rem);
-        let is_non_zero_u = |symbol: Option<Symbol>| {
-            matches!(
-                symbol,
-                Some(
-                    sym::NonZeroU128
-                        | sym::NonZeroU16
-                        | sym::NonZeroU32
-                        | sym::NonZeroU64
-                        | sym::NonZeroU8
-                        | sym::NonZeroUsize
-                )
-            )
+        let is_non_zero_u = |cx: &LateContext<'tcx>, ty: Ty<'tcx>| {
+            let tcx = cx.tcx;
+
+            let ty::Adt(adt, substs) = ty.kind() else { return false };
+
+            if !tcx.is_diagnostic_item(sym::NonZero, adt.did()) {
+                return false;
+            };
+
+            let int_type = substs.type_at(0);
+            let unsigned_int_types = [
+                tcx.types.u8,
+                tcx.types.u16,
+                tcx.types.u32,
+                tcx.types.u64,
+                tcx.types.u128,
+                tcx.types.usize,
+            ];
+
+            unsigned_int_types.contains(&int_type)
         };
         let is_sat_or_wrap = |ty: Ty<'_>| {
-            let is_sat = type_diagnostic_name(cx, ty) == Some(sym::Saturating);
-            let is_wrap = type_diagnostic_name(cx, ty) == Some(sym::Wrapping);
-            is_sat || is_wrap
+            is_type_diagnostic_item(cx, ty, sym::Saturating) || is_type_diagnostic_item(cx, ty, sym::Wrapping)
         };
 
-        // If the RHS is NonZeroU*, then division or module by zero will never occur
-        if is_non_zero_u(type_diagnostic_name(cx, rhs_ty)) && is_div_or_rem {
+        // If the RHS is `NonZero<u*>`, then division or module by zero will never occur.
+        if is_non_zero_u(cx, rhs_ty) && is_div_or_rem {
             return true;
         }
-        // `Saturation` and `Wrapping` can overflow if the RHS is zero in a division or module
+
+        // `Saturation` and `Wrapping` can overflow if the RHS is zero in a division or module.
         if is_sat_or_wrap(lhs_ty) {
             return !is_div_or_rem;
         }
diff --git a/clippy_lints/src/transmute/transmute_int_to_non_zero.rs b/clippy_lints/src/transmute/transmute_int_to_non_zero.rs
index 5df645491ff81..97068efd43cd8 100644
--- a/clippy_lints/src/transmute/transmute_int_to_non_zero.rs
+++ b/clippy_lints/src/transmute/transmute_int_to_non_zero.rs
@@ -16,40 +16,55 @@ pub(super) fn check<'tcx>(
     to_ty: Ty<'tcx>,
     arg: &'tcx Expr<'_>,
 ) -> bool {
-    let (ty::Int(_) | ty::Uint(_), Some(to_ty_adt)) = (&from_ty.kind(), to_ty.ty_adt_def()) else {
+    let tcx = cx.tcx;
+
+    let (ty::Int(_) | ty::Uint(_), ty::Adt(adt, substs)) = (&from_ty.kind(), to_ty.kind()) else {
         return false;
     };
-    let Some(to_type_sym) = cx.tcx.get_diagnostic_name(to_ty_adt.did()) else {
+
+    if !tcx.is_diagnostic_item(sym::NonZero, adt.did()) {
         return false;
     };
 
-    if !matches!(
-        to_type_sym,
-        sym::NonZeroU8
-            | sym::NonZeroU16
-            | sym::NonZeroU32
-            | sym::NonZeroU64
-            | sym::NonZeroU128
-            | sym::NonZeroI8
-            | sym::NonZeroI16
-            | sym::NonZeroI32
-            | sym::NonZeroI64
-            | sym::NonZeroI128
-    ) {
+    // FIXME: This can be simplified once `NonZero<T>` is stable.
+    let coercable_types = [
+        ("NonZeroU8", tcx.types.u8),
+        ("NonZeroU16", tcx.types.u16),
+        ("NonZeroU32", tcx.types.u32),
+        ("NonZeroU64", tcx.types.u64),
+        ("NonZeroU128", tcx.types.u128),
+        ("NonZeroUsize", tcx.types.usize),
+        ("NonZeroI8", tcx.types.i8),
+        ("NonZeroI16", tcx.types.i16),
+        ("NonZeroI32", tcx.types.i32),
+        ("NonZeroI64", tcx.types.i64),
+        ("NonZeroI128", tcx.types.i128),
+        ("NonZeroIsize", tcx.types.isize),
+    ];
+
+    let int_type = substs.type_at(0);
+
+    let Some(nonzero_alias) = coercable_types.iter().find_map(|(nonzero_alias, t)| {
+        if *t == int_type && *t == from_ty {
+            Some(nonzero_alias)
+        } else {
+            None
+        }
+    }) else {
         return false;
-    }
+    };
 
     span_lint_and_then(
         cx,
         TRANSMUTE_INT_TO_NON_ZERO,
         e.span,
-        &format!("transmute from a `{from_ty}` to a `{to_type_sym}`"),
+        &format!("transmute from a `{from_ty}` to a `{nonzero_alias}`"),
         |diag| {
             let arg = sugg::Sugg::hir(cx, arg, "..");
             diag.span_suggestion(
                 e.span,
                 "consider using",
-                format!("{to_type_sym}::{}({arg})", sym::new_unchecked),
+                format!("{nonzero_alias}::{}({arg})", sym::new_unchecked),
                 Applicability::Unspecified,
             );
         },