with a mannlicher M 93 the problem would be the en-block clip for the 6,5x53R. I don't know if it was possible to change it for the 308 win case. the so called irisch mannlicher M 1904 would be the right thing for this modification.
this was a M 93 where the magazine was changed by the Steyr factory for the german M 88 commission rifle clip.

http://www.hungariae.com/Mann04.htm

and

https://www.highwoodclassicarms.co.uk/Firerms%20For%20Sale/0067.htm