You'll probably be OK as you say.
Yeah, that's hot glue and it's perfectly fine to use on the PCB of the PS2. Electrical tape is fine too.
The tip to get wires like that is actually very simple. Place your chip in the correct position on the motherboard (between the 4 copper ground pads at the far end of the board on slim PS2s or between the BIOS and drive controller (LB/BA chip) on older 'chubby' models. Solder all wires directly to the points shown on the diagram obtained from the mod suppliers website and leave them quite long (but don't connect them to the chip yet!) Now if you look at the board, you'll notice 2 or 3 main groups of wires (BIOS, C/DVD Controller and PSOne BGA wires). All you do, is group these wires together and lay them out 'IDE Cable style' and tape or glue them in place. Once they're bunched, its easy to group them, bend them into the appropriate place. The points on the chip are designed so that when you lay them out in this manner, the wire on the inside goes to the first point and the outside wire to the last point - and eventually looks like mine above.
Give it a go, take your time and I think you'll be pleasantly suprised with what you can do...
