Mother Nature is cruel. She attacks the high energy materials first...
Martensitic and carbon steels, for example, will rust if not protected. So, while cleaning up is to be admired, don’t forget to protect tool surfaces afterwards or you will be cleaning rust and pitting the next time.
For the most part, if your die wasn’t giving you trouble at the last use, and you were using some hydrocarbon lubricant like Imperial or similar, you just have to keep the die from getting contaminated before the next use. That lubricant is protecting the working surface inside the die and if you clean it all off, the die may corrode. I live near the ocean so our dust has lots of iron and salt, if I were to clean a die and not preserve it, the next time I see it there will be tears...
Some guys have a body chemistry that is instantly corrosive when they touch carbon steel. For them, cleaning and preserving the surfaces they touch will prevent the grip knurling from rusting. They know who they are... I had one or two guys who were forbidden from touching the equipment without gloves because everything they touched was corroded.
If you ever get hydrostatic bumps from over-lubrication, then just use your typical nylon chamber tools for cleaning your rifles. You should typically already have those so you won’t need to invent die cleaning tools. Even a patch or paper towel wrapped around the chamber brush will do. If you want to take the die to bare surfaces, degreaser, Hoppe’s, or whatever you clean your chamber with will work for the dies. Just be sure to “season” it immediately or spray it down with preservative if you plan to put it in hibernation and plan to re-clean that before you start up the next time.
I have some dies that haven’t been cleaned in over 40 years, and others that have been cleaned and put away each time since those are ones I use when I load for friends who only shoot a few times per decade. Use your judgement and make sure you don’t do damage by over cleaning and not protecting.