Have you tested testosterone and ALL the sex hormones?
What symptoms do you have for low thyroid?
Men when they have low estrogen get joint pain, which is also a common symptom of low thyroid.
Many men on Testosterone replacement have used or needed progesterone. Most tend to get a compounded cream and apply it to the scrotum. Application on the scrotum increases absorption by several times any other location. So a much smaller volume of cream can be used with better effects.
Topicals typically are more of a problem for men than women. This is true for testosterone cream etc. Men also need very little progesterone so I would tend to recommend you ask your Dr about a compounded cream to apply to scrotum. This may achieve best what you are looking to achieve.
Hypothyroidism can't be treated with anything other than replacement thyroid hormones. Progesterone will not repair a damaged thyroid or provide replacement for thyroid hormones.
Do you know what's causing your hypothyroidism? Is it an autoimmune condition?
Although some vitamins/minerals are necessary for proper thyroid metabolism, if you are really hypo, they aren't going to make your thyroid work again.
Why are you going to use them?
I'm having a hard time finding anything on men using them, but I'm going to post some things that may be relevant.
Why anyone shouldn't use progesterone -
Liver tumors
Genital cancer
Breast cancer
Severe arterial disease
Undiagnosed vaginal bleeding
Acute porphyrias
Idiopathic jaundice
Severe pruritus occurring during pregnancy
Pemphigoid occurring during pregnancy
https://www.medicalnewstoday.com/articles/277737#progestin-progesterone-in-medication
Obviously, some doesn't apply to you, but if you have any liver disorders or heart disease, you might want to do some research on it first.
https://www.webmd.com/drugs/2/drug-16557/combipatch-transdermal/details - This says to apply it to the lower stomach, but that's for women. Most of the sites I found in a google said you can wear it anywhere on the low abdomen or buttocks. Do not put it on the breast.
Before using this, have you had your hormones tested? Are you self-treating for something? I would really caution you to not self-treat with hormones, unless you've been diagnosed with something.
Are you trans? https://transcare.ucsf.edu/article/information-estrogen-hormone-therapy
There's no progesterone cream there? :(