A phillips worked for the screws holding the drive in for me. They didn't particularly look like T6 screws, but it wouldn't hurt to have one on hand.
Also, make sure that the Seagate is a SATA drive. Won't work if it's IDE. TC takes 3.5" SATA hard drives, and just format the drive as HFS+ (Extended Journaled) using Disk Utility before you place it into your TC. I think that's all that's required but you could also erase the drive once it's inside the TC using AirPort Utility.
Edit: Just re-read your post and saw the question about having used it for Time Machine. The thing is, you'll have to restart your Time Machine backups anyway assuming you meant that you were using the external for Time Machine backups. Time Machine backs up differently to a networked drive than to a drive attached to the computer so your old backups probably won't work. You can try not formatting it assuming your external's already formatted HFS+ and see if it works. I'm kind of curious now 😛 Good luck! And btw, it wasn't very difficult at all to do the swap. The most difficult part for me was getting the rubber pad off of the bottom of the TC.