Backup without WAL files with Server shut down

Hi,

I'd like to incrementally backup changed files only from a notebook's
pg_data directory to low capacity media (eg.floppy disks / zip
diskds), so I'd like to exclude the WAL files.
I've read about WAL, but I didn't find a definitive answer to the
following question:
-> Does loosing WAL files really matter when all server processes have
been shut down correctly, e.g. with all table data beeing in
consistent state?
And if it does: what kind of information gets lost?

Or the other way around: is it possible to shut down the server, do
the backup excluding WAL, and, if necessary, restore the data, call
pg_restorexlog without doing something bad??

Regards,
Gunter