Delay colonoscopy if I’ll be changing insurance?

tldr: Would it cause problems with getting insured or increased expense if I were to change insurance after getting a cancer diagnosis or any kind of diagnosis that might mean more tests or other kinds of treatment in the middle of changing health insurance?

I’m due a colonoscopy, not due to problems, but due to being over 50 and that’s when my doctor recommended I get one. I called to schedule last month, thinking I’d be in this month, and it turns out I can’t get in until mid-November. This is a problem because my husband plans on giving in his notice at work around then, and does not plan on seeking another job (I won’t go into this as the reasons why could easily divert replies to that topic, rather than what I’m trying to get at here regarding changing insurance providers).

Our healthcare is through his job. I do a little freelance work from home, it does not provide healthcare. I have health and mobility issues that prevent me working full-time or easily working on-site at most workplaces. My question is NOT what to do about my husband quitting, please leave that be. He did say that if I got a cancer diagnosis and was scared about changing health insurance, he wouldn’t quit. But of course, I can’t get in for the test now until it’s time for him to give notice – we won’t have time to get the results back before he quits work, unless perhaps if he were to wait and quit after term and during Christmas break (he teaches at a university). This probably isn’t ideal, he probably ought to turn in his resignation before school goes to break. And he has reasons why he does not want to return to the job in January (unless I already had a cancer diagnosis before he quit), so he will want to go ahead and give notice to end things so he doesn’t return after the end of December.

He says not to worry about doing the colonoscopy and what the results might bring, he plans on getting insurance through the Affordable Care Act (aka ObamaCare, not sure what to call it exactly). Or possibly COBRA at first. And of course, he has no idea how much that will cost or how it would work if I had a new diagnosis in the middle of changing, he’s just in flight mode and needs to get out of this workplace. Again, it’s not an option for me to beg/push him to stay; I have tried to talk to him about that a degree, but there are reasons I can’t go flat out pushing him on this, he is suffering with that job and I can’t get into all of it.

My Question: Would it cause problems with finding new insurance or increased rates if I were to change insurance after getting a cancer diagnosis? Or any diagnosis that would require more tests or some kind of treatment? I should be able to do the colonoscopy now at no cost due to our employer-provided health insurance, which is a point in favor of getting it now. BUT since the results won’t be back in until after he’s given notice, and we’ll soon be changing insurance in some way at that point, will it mean higher insurance rates or difficulty in finding coverage if I end up with a cancer diagnosis? I have no reason to believe I have cancer, no symptoms or family history, but obviously I have no idea what the colonoscopy will find.