In the The High-Risk Refactoring article there is this concise Addressing Risk checklist to keep in mind when refactoring.
During past refactorings (also low-risk ones) I often used almost the same guidelines to help me and can only recommend you to do the same:

✅ Define constraints. How far should I go.
✅ Isolate improvements from features. Do not apply them simultaneously.
✅ Write extensive tests. Higher level (integration) with fewer implementation details. They should run alongside changes.
✅ Have a visual confirmation. Open the browser.

❌ Do not skip tests. Don't be lazy.
❌ Do not rely too much on code reviews and QA. Humans make mistakes.
❌ Do not mix expensive cleanups with other changes. But do that for small improvements.

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