What do models do on the catwalk?

If the OP requires a verb or an idiomatic expression then consider the following:

The models strut (their stuff) on the catwalk:

from the literal meaning of strut (to walk proudly in a way that attracts attention)

Alternatively, models (strike a) pose on the catwalk.

The models walk on the catwalk. Unsurprisingly.

Indeed, from that, one instance of a model presenting an outfit is called a walk as well.

You could use the word sashay.

walk in an ostentatious yet casual manner, typically with exaggerated movements of the hips and shoulders. (Oxford University Press, online)

Examples
"The model sashayed down the runway." (Merriam-Webster, online)

I think it can serve in a figurative sense, so they don't have to be walking in any particular way. Analogously, people marching in a parade aren't always marching in the more conventional literal sense (as in military or a marching band), but may just be walking.