This is an important question, and one that comes up frequently. Using a walker, cane or other walking aid, as they're often called, is a loaded issue for many seniors,
representing a significant loss of independence. Yet, ironically, once someone tries a walking aid, and sees how much stability it brings, they actucally feel more independent than before. So the trick is getting your parent to try it out, so he can learn the benefit. With any walking aid, you always want to have your parent assessed by a physical therapist first. A physical therapist can recommend a type and size of walker (or other aide), and help your parent learn to use it. Sometimes, practicing with the therapist, away from the eyes of friends or family, really helps a reluctant user gain confidence. Maybe you can get your parent to at least agree to be assessed, and to get a walker, with no commitment to use it. There's a good chance that this process will help him over the hump. Once he gets the hang of a walker, and feels more adept using it, the stigma starts disappearing or being less important. It changes to: "Wow, I can walk again!"
Here's a link to an answer to a very similar question from our physical therapist expert, which elaborates on the above. Good luck. You're not in an easy position but others have been in the same spot and really seen their parents change.