Absolutely use time capsule that is the freaking point of having it.
Please tell me you didn't buy a $300 - $500 Capsule and not know what it was for 🙄
Just pop in that disk, re-install, then when you are back in and connected to your Time Capsule, just drag and drop the files into where you want/need them. They will be under backups.backupdb/[Your Computer Name]/Latest, most likely.
Good luck with the re-install.