It seems there is a lack of clarity on the clear aproach to this question.
Let's begin with the Mishna.
Shabbat 22:6, סכין וממשמשין בבני מעים אבל לא מתעלמין, you can administer oils to the body and spread it on the stomach area (for the healing purpose of pain in the abdominal area) but you cannot provide pressure.
This is understood by Rashi as to mean speading these oils with pressure.
This is understood by the Rambam in his perush mishnayos as using עמל on the body, and in Mishna Torah 21;28, he elaborated and rules, זֶה שֶׁדּוֹרְסִים עַל גּוּפוֹ בְּכֹחַ עַד שֶׁיִּיגַע וְיָזִיעַ Which means more of an exercise definition, of Trampaling (similiar to an animal that is דורס) for the purpose of healing to a point of sweat.
We see that, as long as there is no sweat then it is not an issur from the Mishna, that being said walking is permitted even if it does bring sweat (I will not bring a source becuase it is logical). But Jogging is not permitted as it bring sweat similiar to a later point in the mishna קורדימא which is place to go to sweat. Can a person exersise if it is clear that no sweat will come about. (which means sweat from the body, not a liquid, like if someone Jogs in the winter)?
Like Rashi that even a simple hard rub forsure not.
Like the Rambam only if it brings to sweat, altough who is to know if a simple stretch might break a sweat. And we are not talking about drench either because the Mishna which the Ramban made his ruling was talking about rubbing the stomach which will lead to sweat, so even a small amount is assur.
This is two directions beside the abvious uvda dechol.
Interesting clarity from Rabbienu Channanel on 147b in Shabbat, says that מתעלמין is פושטין ומקפלין זרועותיהם לפניהן ולאחריהן וכן רגליהן ע״ג ירכותיהן ומתחממין ומזיעין והוא כמין מעשה רפואה ואסור. וכן אסור לעמוד בשבת בקרקעיתה של דיומסת מפני שמעמלת ומרפאה, Spreading and folding arm backwards and forwards as well as legs on thighs and becoming heated and sweated and this is an act of refuah and prohibited.
As a note:
Let us not assume the only reason Refuah is prohibited is the grinding of spices. We don't know the full scope understanding of our Rabbis.
The three main categories of Exercise is Cardio, Stretch and Muscle training. You can't accomplish Cardio and Muscle training without sweat (see earlier for definition) and Stretch is mentioned clearly by Rabbienu Chananel although with the result of sweat.
I would say from the Rambam and Rabienu Chananel of above that ikkar din, stretch with no possibility of sweat (as you can't do an action if its a ספק issur) would be permitted as long as it is not similar to the way you do it on the weekday as the Gemarah on 147b states clearly סכין וממשמשין בבני מעיים בשבת ובלבד שלא יעשה כדרך שהוא עושה בחול.