Although I think yoga is generally quite silly, it can be approached purely as a set of physical stretching exercises without any spiritual/religious component.
I would compare it to kung fu, which theoretically should have a large Buddhist component, since the creators of the activity were Buddhist monks and the activity was designed purely for religious reasons: monks were not permitted by the rules of their communities to carry weapons.
I am reminded of a "team development" weekend that a firm I used to work for sent me on.
We were all required to take part in a meditation session. The hippy guru guy, by way of introduction, gave us a set of recommendations on physical positions to take during meditation and on themes and ideas to focus on in meditation.
As soon as he shut his yap, I kneeled and said my rosary.
Lesson: as long as you are aware of any New Age/pagan agenda, you can safely ignore it.
I plan to adopt your method if I ever encounter this sort of silliness. Unlikely, because my boss is a straight-ahead normal Methodist sorta guy . . . but I'll be ready if it ever happens!
Why would you put yourself in that position? “Lead us not into temptation”.