do oracle redo logs need to be copied when all other data is copied to a new disks?
If you are using ASM, you could even do this online by first adding the new disks to the current diskgroups, rebalance the disk groups and drop the old SAN disks from the diskgroups. During this drop, the first thing that happens is - again - a rebalance action in which the data that is on the dropping disks is moved from those disks to the new disks. A very powerful feature, not sure if it can help you.

If it all has to be done using FS copies, it still can be done online, if you are running archive log mode. Since 11g RMAN can clone from an active database, also very powerful.

FWIW: some applications check the controlfile and complain if it is changed. This is part of a check for licenses.

Short answer for you question, you need the online redologfiles. The archives are only needed for recovery operations so they should remain accessible, not perse on the new SAN. A regular backup would be ok. Copy the online redo logfiles and use RMAN for the copy of the database since it handles everything that needs to be done in a good way.