Hey Lando,
Thanks for your question and welcome to the community.
As long as the receiver/remote for the ceiling fan can be by-passed, then you can attempt to by-pass it and wire it via the 3 speed switch as you stated.
However, some receivers are fully integrated with the ceiling fan, so by-passing may be difficult or impossible.
If there is a receiver in your fan above the motor inside the ceiling canopy, this is the version that can be completely removed and by-passed.
If not, I can't say with certainty if you can successfully setup everything this way without getting more information from you. Namely, what's the brand/UPC/SKU/Model number...whatever you can find on the sticker on top of the fan.
I can't stress this enough, knowing what type of ceiling fan can greatly assist you in solving, troubleshooting, and ultimately repairing your fan.
As long as everything is safely wired separately to its respective switches, you can do this. But, to make sure, know what your fan is first and go from there. Once you know what ceiling fan you have, then you can contact its manufacturer for more information.
Update on your progress and even what type of fan you have, and we can assist you further.
Joseph