Old installer is offline when you install it.
osu! Is completely portable, you can copy the files and it'll still work, even on a USB.
You should copy
- \Songs\
- \Skins\
This is all you really need, but if you want the collections, settings and relays included copy these
- \Replays\
- \Export\
- \Screenshots\
- \osu!.<username>.cfg
- \collection.db
For the scores, you need to copy
both of these
- \scores.db
- \Data\r
*\Data is a hidden folder