At .045 differance, I wouldnt worry to much about it.
I doubt it would effect the way it meshs to the other gear. I would just do a very carefull set up, and roll it over by hand and look/feel for any binding. You say you have ajustment for back lash, so in that case, you should be good to fit the new gear up. Just remember, after your gear is fit into place, turn the setup by hand. Check for binding while turn it over. The end gear train should have other gears in there, that have no ajustment for BL. See what they have, and try to match it. If you want to see the effects of setting the BL loose, or tight, you could pick up some gear marking compound from a automotive supplyer.It would show tooth contact patch patterns at various depth settings. Its a yellow paste, you just brush on , and roll it back and forth, then look at the pattern.
The tooth profile on the replacement gear, if it is indeed the same would show you how well is meshes together. If you can get it setup to the point where you feel no binding, and a reasonable BL setting, only then turn it under power. I would run at the slowest speed, and work your way up from there. If your lucky, you should be good to go.
Good Luck