I scanned mine - didn't do them any harm whatsoever. Mine didn't come out that great though, so I bought a cheap little photo album from Boots (£3) and put the originals in there - that way I didn't have to worry about people handling them, and could show off the originals.
There's a sign up in the hospital telling people not to laminate (it's almost like old fashioned fax paper they use to print the photos) ... I'd be devastated if I'd ruined mine!