Most answers on this forum will likely focus on use of the word "can" rather than "may". The more polite form would be for your son to ask permission, as in "May I skip my nap this afternoon?".
That said, the use of "can" is not incorrect Link
To expand the dialog your son could try to justify or mitigate the nap skipping with reasons like "I'm not tired enough", "my friends are playing now", "yesterday I did not sleep at all", or "I promise to go to bed on time without argument".
The question veers into parenting style very quickly. Some parents will want the child to state a request and reason, then abide by the parental decision. Others will invite the child to make the choice, but accept the consequences (e.g. "You can decide skip the nap, but you loose the privilege next time if you're cranky at dinner time or skip any chores later.").
As for language, it is now popular to stick with your native language at home, and leave the English learning to school and the playground. Your English may need focused adult effort, but your kid will absorb all but the finer points on the playground.