1) When your rifle was made, the 7x57 was pretty much the going thing (latest/greatest), so a "7mm" marking was quite common THEN, as opposed to NOW, when there's quite a few 7mm/.284" on the market.
2) If your gun has the military sights, the lighter (140gr), faster commercial ammo will be hard if not impossible to zero, w/o changing the sights - since (as posted above) they were AFAIK regulated for a bullet weight/trajectory of 175gr - again, the onlyest slug available for military &x57 rifles in 1910.
3) ANY commercial 175gr JSP slug is loaded for the weakest 7x57 rifles ever made - they are NOT "military/heavy" loads - and so will do just fine for whitetails, even at short range (provided you can hit them).
4) The yardage on shooting ANY cartridge can be stretched - the problem is:
(A) Actually being able to hit someting "out there", and
(B) Actually having enough energy "out there" to humanely kill a game animal.