That's a good idea ^^
Hitting out something made of aluminium with something made of hardened steel over a small surface area that is a tight press fit is never a good idea. The proper tool is designed to spread the load over most of the headset surface. Used properly it should ensure the headset comes out straight as well, hammering a screwdriver twists headset making it tighter and that's how headtubes crack.
I have the Ice-Tools headset remover it cost something like £12 and the 1.1/8" version can be used on 1.1/4" as well.
Same here; I've got the Ice Toolz and have used it 1 1/8" and 1 1/4" successfully with head-tubes as small as 100mm.
Another top-tip which I have done is to cut a V-section in the very thick wooden work-bence and line it with rubber. I then place the frame down-tube or top-tube as close to the head-tube as possible in the V-section. This holds the frame properly and doesn't dent the tubes at all (even very thin AL) as the force is spread over a very large area. Usually, one or two sharp whacks with a hammer and the cups fly out.
I cringe when I see people trying to remove head-set cups with constant bashing when the bike frame is badly held in a bike stand by the seat-post.
Favorite quote on Retrobike:
Not worth the petrol to take it to the tip so it's down to the angle grinder to make it small enough to put in the wheely bin.