Upgrading to a slightly heavier string gauge (as you have proposed) will not always necessitate a new set up. Upgrading to a much heaver gauge will increase the likelihood that adjustments will be needed.
There are two main things to look for when going to a heavier gauge string.
First, heavier strings will result in more tension on the neck and could cause the neck to bow a little more. If that were to happen, tightening the truss rod very slightly by turning it clockwise would compensate for the added string tension. You won't know how the new strings will affect the amount of relief (height of strings above frets in center of fretboard) until you have tuned the new strings to pitch. If you do decide to tighten the truss rod, loosen the strings a little before tightening. Most likely, going from .09s to .10's will not necessitate a truss rod adjustment (or only a tiny bit if at all).
Second, heavier strings have a larger diameter and may not seat properly in the string slots on the nut. Most guitars with factory nuts have the string slots cut fairly wide to accommodate a range of different string gauges, so most likely this will not be an issue. Again if you were to go significantly heavier, it might be necessary to enlarge the width of the string slots in your nut. That is a process that requires a special set of files and some expertise. If you get the slot too wide or make it deeper, it could have a negative impact on your tone or result in rattling or buzzing due to the string being loose in the slot. You probably won't have to worry about the string slot size to go from .09s to .10s.
If you had an adjustable bridge you could check the intonation after changing to heavier strings but that is a do it yourself adjustment. If you can change your own strings, you can adjust the intonation. The slight change you proposed should have a negligible effect on intonation so an adjustment will probably not be needed there either.
I think you will be just fine with no adjustments at all. Try it and see.