You need to post your inquiry under immigration. I can tell you what is happening from a criminal perspective. A class C assault is simple assault - meaning that you touched someone without hurting them and that you knew if you touched them in the manner you did, they would find the touch offensive. Sounds like it was the right charge.
What can you do from a criminal perspective? Pay the fine = final conviction but no fingerprints. Ask for deferred prosecution and offer to take an anger management course - after completion of the course and the passing of the agreed upon time, the case is dismissed. You can then get the case expunged.
I know that assaultive behaviors are VERY bad when it comes to immigration consequences. I have heard this includes Class C assaults. You should consult with an immigration lawyer (more important than a criminal lawyer at this point) to determine what is "okay" with immigration as far as disposition.