If you set about crytpozoology is a scientific manner as
@Mikefule say, the course would vaporise from it's own examination of the field. All the students who joined up thinking they were going to be talking cryptids with other believers would discover they're doing actual science and probably leave, because, 'science doesn't have all the answers'. Or summat.
This is possible in some cases. There will always be students who choose a course based on their casual interests and hobbies who give up when they find it is not what they expected.
However, my point was that cryptozoology could be an interesting and diverse subject for a degree course, although one of the problems would be that it is so multidisciplinary, encompassing sciences, the arts and humanities. There is plenty of scope for genuine and respectable academic study.
Sciences and maths: analysis of energy budgets, food supply ecosystems, minimum sizes of viable populations. If there were to be an unknown species in Loch Ness, what would be its minimum requirements in terms of breeding population, volume of water, or mass of prey species? Which cryptids are "plausible" from these points of view, and which are not?
Psychology: What is it that inspires some individuals to believe strongly in the existence of certain cryptids in the absence of evidence? What inspires other individuals to believe in certain cryptids despite the clear evidence to the contrary? What inspires some individuals to believe in the Yeti but not Bigfoot, or vice versa? How does susceptibility to these beliefs tie in with phenomena such as conspiracy theory? Are the believers in "fairly plausible apemen" psychologically different from believers in cryptid megafauna, or from those who believe in the weirder theories about cryptids from alternative dimensions?
Sociology: Is belief in cryptids associated with certain age groups, one gender or another, different socioeconomic backgrounds, or cultural backgrounds? Do people from different backgrounds tend to believe in different kinds of cryptids? Does the nature or prevalence of belief in cryptids change in accordance with political or economic events. (Comparison here with widespread belief in alien origin UFOs at a time when many people felt the world needed saving from imminent nuclear war.)
Social history: How have beliefs about cryptids changed throughout history? For example, in mediaeval Europe, were all cryptids described through the paradigm of Christian belief? How did our attitude to cryptids change as society became more secular and an understanding of science became more widespread?
History: Studies of actual historical reports, and an understanding of historical context that may help us to interpret those reports. In an age where dragons were a common motif, were sea serpents described in terms that made them more dragon-like? Now that most people have some idea about dinosaurs, are descriptions of cryptids more likely to be influenced by perceived similarities to known dinosaurs? The Loch Ness Monster is a fine example. It went from being a "water beast" in the time of St Columba to being "probably a plesiosaur" when dinosaurs became well known, to being "perhaps an eel" when people started to understand the basic ideas of ecology. Have witness descriptions of the LNM changed accordingly?
Literature: Many reports are in printed sources. These need to be compared and analysed, and placed in context, using the sort of skills that might be possessed by a student of literature or the classics.
Mythology: There are obvious feedback loops between "natural myths" and "contrived fiction". Fiction adapts myth for its own purposes, and myth absorbs tropes from fiction. The most alarming case is perhaps the way that Slender Man (of known fictional origin) became such a powerful myth that it led to the 2014 stabbing incident.