If you have a screwdriver that fits perfectly as in fully in and no play, the screws shouldn't be an issue
Worth heating up the bracelet, they are using some type of loctite / something similar. Hair dryer on the bracelet for a few seconds or, alternatively use some hot water and dangle just the braclet into it and same effect. Make sure you buy a decent slotted screwdriver set.
Don't buy the multi-sets they're usually crap. Find them individually on amazon.
"Slotted screwdriver 1.2mm" - replace 1.2mm for 1.0mm 1.40mm 1.6mm and then you've got a full set.
The slotted part means the tip is flat, not sharp, so you dont scratch the links etc.