You'll have to hit it pretty hard to break it, and a screw driver handle shouldn't affect it in any harmful way. It's effectively a soft blow hammer - now if you were gonna try to drive it out with an actual hammer or something - that might have an effect. It's hard to explain, but you're just giving it a good thump. Or you could give it a fairly forceful push - that's pretty much all the other type of compressor is going to do for you. And you're not putting a side load on it that way, so unless they're seized in the guides you're not going to bend them or anything. Give it a whack and see what it does. Worst case scenario is you screw up *one* valve - you'll know what NOT to do if that happens.
I have a smallish piece of bronze that was going to be scrapped at a place I used to work that was kinda shaped like a hammer, that's what I used. If you have a decent sized piece of aluminum that would work to. You just don't want to use anything that's harder than the valve material to smack the valve head. You're basically giving it a good shock to break it loose, once that's done it'll come right apart for you.
It's a lot the same concept as removing a collet from a Bridgeport knee mill. The R8 collet is locked into the spindle by the drawbar and the taper and kept from spinning by a key. You loosen the drawbar but the collet won't just fall out, you gotta give it a little shock. Here's a couple videos to show what I'm talking about:
You can see it's a decent whack - it's not like driving a nail or anything, but it's not like you're tapping someone on the shoulder. Think of the drawbar as the head of the valve and the collet as the keepers. Give the valve a whack and the keepers will suddenly let go.