I haven't re-handled an S1, but yes they can be done. Others have done it.
You can also purchase blade blanks from Fallkniven, I haven't checked to confirm, but I do believe the S1 is offered as a blank.
The blanks have a wider tang so putting a handle on them will result in a full tang knife.
Removing the handle from a factory knife will leave you with a narrower tang, but still usable.
Depends on what your preference is for handle depth.
Check out the Fallkniven forum over on knifeforums.com for more info on factory re-handles.
http://knifeforums.com/forums/showt...ost/1696249/hl/rehandle/fromsearch/1/#1696249
Kevin
EDIT: Yes, the S1 is offered as a blade blank