I have never heard of a .358 Win Mag.  The 88 was offered in .308W, .358W, .243 and .284W.  It was a stout action but probably not strong enough for any magnum loads.  The first years the back of the thrust block was in a clover leaf shape which weakened the wrist of the stock, causing numerous failures.  This was rectified in 1959, but I still don't see the strength being there for a magnum cartridge, even if one were available back then.
I would suggest making a casting of the chamber and measuring it - I would be very surprised if it was anything other than the .358 Winchester.
-Kees-