Might be a bit tricky.
All recommendations are based on my own experience and anecdotal evidence - nothing I say is guaranteed to be 100% valid:
Shipping Vendors:
Since private companies like Fedex/DHL/etc. do the customs declaration for the packages they transport they are in a way liable to do it correctly and sometimes seem to get stricter controls or don't even accept the package if there are any suspicions.
Customs Declaration:
Undervaluing/Gift is pretty much a gamble. If its checked by customs and its not a franken but just a regular rep it pretty much surely will get destroyed. Austrian Customs are quite strict regarding all this.
Is the watch slightly used/M2M? if so, package and setup everything like it will be repaired. Put a letter in there detailing some problems/broken parts etc that have to be fixed. Pretty much make the whole package look like "broken watch inside" without actually writing that - you get my vibe?
Maybe think about using a triangle shipping provider (Czech Republic, Netherlands, Belgium, etc. has several) and use a small package (all packages that ever got siezed for me where larger ones like 2 rolex boxes for example. the usual 1 or 2 watch size packages from china (via 4px/Beglium or UK Triangle before Brexit) all came through safe.
If you or the other guy by any chance know a person that travels from thailand to austria in the near future definitly give it to him to take it with him on the plain. Getting through customs with a fake watch in an airport (for personal use) is totally fine and legal. Only when they come via postal services things start to get tricky.
Maybe some other austrian members on here can give out some recommandations too.