Get the headspace checked, use commercial 6.5x55mm ammo (or surplus if you can find it - good luck), and enjoy!
yes, the old gun's metalurgy isn't up to modern standards...yes, the swede round is a 40Kpsi pressure class, and yes, its not as fast as higher pressure (and more modern) rounds.
Swede rifles were considered primo for their era, because Swedish steel was the "best", in those days. Its a 95 Mauser action, which lacks the "safety lug" found on the 98 Mauser (which only does anything when something goes badly wrong, anyway), and lacks the flange on the bolt shroud to help deflect gas (again, only when something goes badly wrong), and its cock on closing, which is something some people don't mind.
Something to be aware of, most (if not all) the Swedes were set up for the 160gr military ammo, and will shoot high with other loads. And they were zeroed for 300 meters, if I remember right.
Replacement front sights of different heights are available, and I would recommend checking into getting one if you plan to shoot a 140gr (or other weight) bullet.
The 6.5x55mm has a long history, and an excellent reputation, because they work well, are accurate, and have low recoil (compared to most other military rounds of the era). The Swede's long bullets hold velocity very well, and actually shoot flatter than many .30-06 loadings.
DO NOT try to hot rod that rifle! If you want more than it is designed to give, get something else. But what it is designed to give is plenty for almost anything, and it will still give it, as good as it did when it was new (assuming it's in good mechanical shape).
If you can shoot open sights, you've got an excellent woods gun for deer, just the way it is, and quite capable of 300yd shots, if you are!
I have one of the long rifles (1917 mfg) and can easily tag the 400yd gong at the range, without even raising the sights! (140gr speer bullet and mid-level charge of IMR 4320).
All else being equal (and it almost never is) bigger bullets tend to work better.