A few remarks regarding your motivation:
Be aware that some up votes are not following a thorough investigation of your answer. For some users, it's good enough if the answer sounds good. Your post can be totally and provably wrong even if quite a few users agree with you.
In my opinion, a single up vote isn't enough to warrant special consideration. Your edit gives the user the opportunity to reconsider the vote anyway, as votes can be changed after an edit. If the answer was accepted, and therefore stands out as "This actually helped someone", it might be different.
In a way, leaving wrong information directly visible, even though someone liked it (for whatever reason), pollutes the web. We endeavor to create a useful source of correct information on the web. If the information in your post is wrong, just remove it.
Previous versions of your answers are archived anyway until the end to time and anyone can access them by clicking the edited link below the post.
Of course, if your intention is completely removing the original post so nobody except 10k+ users and diamond moderators can read it (and laugh about you), nuking that answer and creating a new one is the only way to do this.
My suggestions for the implementation
Simply edit your post. If you still want to make a previous version of your answer more visible, you can also add a simple reference to it to your completely revised answer. You can link to specific revisions of a post:
- Click the edited link below the post
- You see a list of revisions. There's a chain link symbol next to each. Click it, and you go to that revisions permanent address.
- Copy the URL and link to it in whatever form you you deem appropriate, e.g.
(Here's tons of correct information you carefully researched)
This answer was very different (and actually not correct) in the beginning. See here for the original version.
If you want to be really thorough, as I like to be in Meta discussions when revising my answers, you can record the up/down votes at the time of the edit as e.g. +1/-0. This allows others to judge the value of your edited post.
(The example's a question, I know. Didn't find a good example quickly)