Profesor Trelawney's classes do not seem to involve magic spells or wands, at least in those classes shown to the readers. I don't remember her mentioning anywhere needing to know about spell or wand work, to succeed in her class.
She does say that a true seer needs to have the "inner eye", what ever that is, and the true predictions that she does make regarding Harry and Voldemort seem to be things even other wizards might not have been able to do.
However, we are shown that her class also involves reading tea leaves for divination, which just seems to be some form of pattern recognition.
In fact, Firenze's class also mostly seems to involve observing stars, recognizing patterns and knowing what certain patterns mean, rather then involving actual spells and magic.
Would muggles be able to learn and perform some of these divination methods? Would a muggle be able to make an AI pattern recognition software to scan the pattern in tea leaves and predict the future using a computer?