I did that many years ago and used it for 25 years as my primary deer rifle and it never let me down. Finn Aagaard called it the perfect deer cartridge. It was one of my gunsmithing school projects.
First a bit about the 6.5x55.The Scandinavian military cartridge, with a Krag for Norway and Mauser for Sweden.There were some slight differences between the two and that was finally adjusted to the 6.5x55SE .
We then had ,in the USA, a lowering of the SAAMI pressures because of the old guns .This dropped velocities down about 250 fps. Then American companies started to load it but used the .473" head instead of the .479 " head of the original !
I think now the cartridge is for hand loaders as they wimped out the loads .For a reasonable load you should be able to get with something like 4350 , and a 140 gr bullet 2750-2850.No sense in pushing it , it's not a magnum and does the job without high velocity, recoil or muzzle blast !
Now the rifle - Mine is a '43 Obendorf M98 .For the work I was doing I wanted to be sure so I re heat treated the action [the hardness varied quite a bit and wartime quality became worse throughout the war]. No opening of the boltface was necessary.The barrel was made so both inner and outer shoulders seated to the receiver for max rigidity. The action and 2" of the 24" barrel were glass bedded again for rigidity.Canjar trigger added. A 1/2" gun !!!
Decisions to make - chamber 6.5x55SE or American .473" head .I would choose the SE but then use European brass. I throated for the long factory 160 but never used that .This long throat didn't effect accuracy [throat diameter is very important which many ignore]. I've always thought the 140 was the ideal bullet weight.
I suppose you could use one of the other 6.5s but I like using and trusting something that's been around for 100+ years.
A great cartridge [ for handloaders now] you'll love it !