In the passage you quote, the author is making an apology (perhaps a mock one, intended to point something out rather than truly apologize) for making two references to snakes. When the author says:
Sorry, I normally try to limit myself to one...
We know this is not the first occurrence. I might say something like this upon taking a second serving of a dish, when I know I shouldn't, but can't help myself.
To find the first instance, look backwards; in the previous paragraph of the article in question, another reference to snakes appears:
It took me a few minutes to wriggle into it — picture a film of a snake shedding its skin, played backward — but once I did, the women in the group were agog over my impressive physique. At least I think they were; it was hard to tell because most of them couldn’t stop laughing. [n.b. emphasis added]
Snake metaphor can be understood if you take snake to modify metaphor - so it's just a metaphor involving snakes, as train metaphor would refer to a metaphor involving trains ("This answer is running off the rails," "No point in stopping now that the train has left the station!"). Though the author's choice might be odd, or these might be weird metaphors, snake metaphor is not equivalent to any weird metaphor.
The two metaphors in the article appear when the author likens himself to a snake shedding, and then likens the shirt to a python. Because of his description of the shirt as one that "shapes and firms", and his difficulty getting into it, we know that with the python reference he probably doesn't quite mean it's heavy or hot, but that it is constricting about him like a python suffocating its prey.
Finally, can we say snake joke? While a joke and a metaphor aren't the same, the author's use does seem to be intended humorously. The choice of reference to snakes is also funny because, given the context about running in nothing but underwear, it brings to mind euphemisms like trouser snake for a body part that one might fear would be less than adequately covered without trousers. So I think we might, indeed, assume this is a bit of a snake joke.