Wearing a hat 6 weeks after your FUE should not affect the transplanted grafts anymore than your regular hair. After about 5 days, transplanted grafts are part of your skin and living tissue. I allow my patients to wear loose fitting hats 5 days after the procedure. After 2 weeks they can wear a hat as much as they want.
As far as we know, most of the body depends on oxygen that is processed via the lungs so your scalp is not going to be deprived by a hat. No science has shown hats to cause or be related to hair growth. After a procedure, they do not like hats because they mess with healing tissue but not because of the oxygen.
We give out hats to our patients for their elective use of them. They are not fancy, just trucker hats but they are clean and new. You can wear a hat anytime, just don't let if rub on the frontal hairline when you wear it.
Wearing hats do not affect hair loss. Wearing hats do not affect hair growth. But if your doctor says don't wear hats, then follow your doctors advice.
Wearing hats after a transplant
One of the biggest myths or misconceptions is that wearing hats deprive the scalp of oxygen. That's not how it works
Wearing a hat is ok if the first two weeks is fine provided it is put on and taken off with extreme care. After 2 weeks, a hat can be worn any way you like
Hairs get their oxygen from blood vessels inside the scalp - not from diffusion from outside to inside
2 weeks post surgery return to normal activities
After two weeks post procedure there is nothing you can do to either help or harm the follicles unless you bump your head. Patients are free to go back to a normal routine at the two week mark post procedure.
Hats are fine 2 weeks after a FUE hair transplant
The risk of graft dislodgement is greatest within the first 5 days after a FUE hair transplantation. I err on the side of caution and advise my patients to avoid hats (i.e. friction on the transplanted grafts) for 1-2 weeks after the procedure. The hair follicles get oxygen from the capillaries (red blod cells) that supply the hair. - Dr. Keaney