I think it's a neat idea to try just going with one ball in order to work on your game more. However, there are a couple of things you have to keep in mind:
1) Team impact. If this were a singles match-play league or something, you'd have nothing to worry about here. However, since you have teammates, it's probably good form to tell them of your plans and see how they feel about it since your approach could impact the team standings, which = money, bragging rights, etc. Hopefully they're all for it, but it's probably best to at least ask them first.
2) League complaints - If you start off doing this, are unhappy and then switch back to using other balls, some in the league may look at what you're doing as sandbagging. I wanted to do something similar years back, so I started using plastic as my only ball. Obviously, that made me have to be very accurate and creative in order to get the ball to hit. Some people were furious because of the impact of plastic on the pattern, and others thought it was an attempt at bagging even though I averaged over 200 while doing it. In any event, again, you may have to commit to doing this for the entire season in order to avoid such talk/accusations.
In the end, you're the bowler, so as long as you're not doing this with some ulterior motive, you should be free to use whatever ball or balls you want in order to work on improving your game. I applaud you for doing so, but I wanted to throw those things out there as food for thought. Good luck no matter how you decide to proceed!