From what I know and have seen when this was explored heavily in the node ecosystem there are three main techniques to making a version manager.
1. Use global symlinks. Pros: Simple, no mucking with environments, and all programs can see the change. Cons: All programs will see the change.
2. Spawn a subshell with environment variables set. Pros: No messing with teaching people how to source bash scripts. Cons: Yet another shell and process. What happens if you change multiple times, does it keep getting deeper?
3. Write a bash function. Pros: Edits environment in-place for the current shell. Cons: Installing can be tricky as most people don't know the difference between sourcing and running a script.
In the early node days we had a champion of all three methods. My nvm was the source a bash function style. Isaac made the subshell option with nave and TJ Holowaychuk made n which went the symlink route. As far as I can tell, nvm is the only one that's used heavily anymore and pretty much every node getting started guide tells people to install nvm.
When I made it the instructions were to clone this repo somewhere and add a line to your bash profile to source a script in it. Nowadays people just use the contributed installer script which tries to do all this automatically.
Popularity doesn't mean a technique is better or best, but I hope my experience can be at least helpful. If you do go with a nvm style path, be sure to read up on how the install instructions are worded and look at past issues where people were confused.