Just installed a no-solder into my version 4 PS2. Went out and bought a gameshark2, new version 3.

Cant get backups to even start. After doing some searches I don't see anything regarding this new version of gameshark2. Will it work or do I need to buy a different version? Should I buy swap magic instead?

Gameshark3 will not boot burnt things with that chip.
Look for a gs2 1.9 and above. The alternative is to just get the Swap Magic disks. BOth will accomplish the same tasks, but the gameshark would be able to do more, much more (use codes, avoid boot probems etc).