In general, I would be hesitant to switch the grade of stainless steel used. You are asking to switch from a more unique grade to a common grade. There was probably a good reason why the grade 420 was chosen for the original design.
With that in mind, the differences between the two grade seem to mainly be that 420 is harder than 410 (see these references: 410 and 420).
From what you have described of the requirements (e.g. fatigue is an issue), it seems strange that grade 420 was originally specified. Typically a harder material is more brittle and has a lower fatigue strength. Using that one factor, it would seem that 410 would be an OK substitution. The original designer should have known this though. There is probably a good reason why grade 420 was chosen.
If you can't ask the designer, it would not be a good idea to substitute a cheaper material.