want to know what the cheapest way

[ALLREADYDONE (imported)]

Depo-Provera will do just fine, you will probly want get rid of your sex drive alltogether at first and if your wife is comfortable with that maintain it. I have no experance with chemical castration since I opted for surgical castration. The results are similar, and I am sure your wife will be much more comfortable. It is very unlikely you will be bothering your wife at all since errections will most likely be a thing of the past.