@richandjanice,
That is a great question; it will be interesting to see what other members have been told. I did not have a mastectomy, but had surgery on my left breast and a few lymph nodes removed. When I had chemo, they always used the right arm, and veins in that arm are a lot harder to get a needle in.

Now, if I have a blood draw or IV and I mention that I had lymph nodes removed, the tech drawing blood will not use the left arm. I do not have any lymphoedema in my arm.
Of course, I will follow my provider's advice most of the time and avoid the arm with lymph nodes removed, but sometimes I do not mention it and let them use the left arm because it is so much easier to draw blood from that arm. This is often the case during a procedure or in the ER; I do whatever arm is easier.

I did find an article on the subject on a Phlebotomy site.
https://www.phlebotomy.com/phlebotomyblog/blood-draws-after-mastectomy-what-new-research-shows.html
It does reference a few studies on the subject with links to published articles on PubMed