Alternating between left and right or no?

Strange topic for a title I know. What I mean is: When practicing grease the groove exercises such as one arm pushups and pistols, should I first do a set with my left arm/leg, and then do another set with the right arm/leg or should I do two sets where I’m alternating between left arm/leg and right arm/leg?

Untill now I’ve been doing the former but I read Jack Arnows one arm chinning guide where he talks about alternate comedowns and Was wondering if I do the same for other exercises, would it lead to quicker strength gains? Or would it just compromise endurance?

At the moment I can only do an arm out style one arm pushup but was thinking that if I started alternating between left and right, maybe I’ll finally be able to do a one arm pushup with the elbow staying close to the body.

What about when doing a PTTP type programme and doing an exercise such as the side press?