I might be wrong so do your own reseach but as far as I know Mohair is a rubber bonded layered cloth so under no circumstances should you use a spirit based or chemical cleaner as it can damage the water repellency and that would apply to the inside as well
I think the cloth is very similar in nature to Makintosh fabric which I have on a few coats
Only a specific cleaner designed for soft top Mohair is best used which I think will just be a mild soap type cleaner
Soap and Luke warm or cold water might be a cheaper alternative