Also, use a correct sized screwdriver, if you do no have a set, Harbor Freight sells just about any sort of screwdriver you could want and most od it is very good quality, with a lifetime warranty on most if no all.
The 'give away' screwdriver sets that you can pick up from time to time free, with a purchase are good enough and less than $4 but two other options you might visit is the plastic protected "electricians" set, as the plastic shaft will make interior contacts no big deal, but they still have metal heads exposed.
Getting these for about $10 might just save your life of the life of someone using them in the future, as they are rated up to1,000 volts and who amongst us does no need a insulated screwdriver around the house, truck or for a Vivitar Flash repair, but never actually buy one, risking electrocution with the wrong tool, forever?
Get the full sized set, they also offer a precision set for about $9 but it's too small for this game.
The third set you might look at, especially if you never need to fool about with electricity, and electrical gadgets, is the blue, bolstered set, which is a good general set with fine enough smaller fathead (3/16" up in slotted) to do the job you need and, you'll have a set drivers that can be torqued in place with a socket or pliers for frozen screws on non-camera kit.
$12.
Make sure you magnetize the head of the screwdriver you'll be using to remove/return screws, and if you cock the lens with a driver, first set the lens, face down on a rock solid surface and cover the opening to the lens interior with your 'free' hand so no slip of the screwdriver will stab into the inner glass/workings, advance the mechanism.
It's an easy repair and you'll be fine, just take your time.
IMO.