For those who like numbers...case volume capacity wise....
9.3x57...63.3 gr H2O
9.3x62...76.4 gr h2O
About 13 gr H2O difference
358 Win...57.2 gr H2O
35 Whelen...70.9 gr H2O
About 13 gr H2O difference.
About 6 gr H2O difference between the 9.3 and 35 cal per case size. Not hardly enough to get in a sweat about unless you like to split hairs.
As stated above you...would gain 100 to 150 f/s...more or less...and 36 gr more bullet weight by going from a "standard" 35 cal 250 gr bullet to the "standard" 9.3 cal 286 gr bullet. Going from 9x57 to 9.3X62 is a fairly easily done re-chamber. Basically you gain a larger dia. bullet, more bullet weight and more impact energy over the 35 cal which is why the 9.3x62 is such a good cartridge for 95% of all the worlds game...and so is the 35 cal. One is an American meat and potatoes caliber and one is a European meat and potatoes caliber...so to speak...but your 9.3x57 will handle the chore without any problems also and has done for many years...on both continents.
If I had an original 9.3x57 chambered rifle I wouldn't mess with it at all...just enjoy it.
Whether it is economically feasible to re-chamber it, or whether you want to at all in your application, is what this sport is all about. I have a milsurp M98 waiting in the corner waiting for the holidays to end to order a 9.3x62 chambered barrel from Lothar Walther...I don't "need" another large caliber...my rack is full of them...but I'm filling out all those calibers I always dreamed about, wanted to have, but never built.

In my younger days I used to walk/run the high school football stadium bleachers with a back pack weighing from 40 to 80 lbs or whatever I calculated would be the weight I would haul during long backpacks or hunting/fishing camps. I started low of course, but I never thought about using a weighted walking stick. That is a very good Idea. I usually carry an 8 to 10 lb rifle or shotgun all the time when I am beating the woods because I live 35 miles out in the boonies in bear/cat country so at least I get some arm workout, but I don't haul any "extra" weight...not that I shouldn't.
Happy Holidays
'Njoy