I have a project and documentation for it.
My command writes “[…] whom he or she wants to participate […].”
Is it correct to write he or she, or should I write another word, such as user, person, or human?
Is there any difference between American English and other English dialects?
You don’t show the rest of the sentence, so I cannot say if it should be who or whom, but you don’t need to write he or she. Just write “who[m]ever wants to participate.”
Whomever is used as object of a verb or preposition; whoever is used as subject of the sentence.
He was free to marry whomever he chose.
Whoever says that is a liar.
In your case, it could be, for example:
Whoever wants to participate is free to do it.
We welcome whomever wants to participate.