Texas Jack;
The R in the 7x57R simply denotes it to be a rimmed shell while the 7x57 is rimless. Most break open guns use the rimmed round for extraction while most bolt rifles use the rimless for better feeding. Otherwise dimensions are the same. You will not endanger the gun with the rimless round but as you noted it is hard to extract the empty. This is of course conditional the chamber was properly cut to headspace the round on the shoulder but it likely was.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra