If you're going to do it, definitely change the jumper. Note: I'm not an EEPROM specialist and Rainbow has said that for some devices the programming voltage needs to be present on boot - maybe this is just when updating ESCD, I don't know. So I would change the jumper to 5v with the power off but if your friend's machine then fails to boot, change it back to 12v and set it to 5v once you've removed his BIOS ROM.
This is a DIP ?
I use a flat bladed screwdriver and work it in carefully keeping the chip (and the screwdriver blade) as flat as possible. For your friend's machine, take the chip out with the power off and leave it slightly pressed into the contacts so that you can remove it easily once it's booted.
If they are PLCC, I use a special tool with a little foot on the end which you slip down one corner of the chip and hook the chip up from underneath, alternate corners a bit at a time.