This is the thyroid forum, and while I'm not an expert on perimenopause, I would certainly say a couple of things.........
First off, all the hormones in our body must work together and if some are off, it could throw everything else off, as well.
Secondly, I've never heard of perimenopause causing hoarseness, but hypothyroidism most certainly can. Have you had any thyroid testing done? You would need to have, at the very least, TSH, Free T3 and Free T4 tested, and depending on those results, you might want to go further. I'd also recommend a thyroid ultrasound to see if you have nodules that could be causing the hoarseness.
Do you have any other symptoms consistent with low (or high) thyroid?