The decision as to whether or not to clean any artifact is a tricky one. You're faced with the problem of wanting to have the hat cleaned but can't be certain that any cleaning procedure will damage it...a very real possibility. Are you going to preserve the tam or do you want to wear it? That has a bearing on how to proceed.

The least radical thing to do would be at least to give the tam a good airing. Placing it in front of a fan set on low for a while usually helps some. Past that I'd consider finding a professional fabrics conservator and get their opinion. If the thing is precious to you, turning it over to the dry cleaners on the corner might not be the best course of action.

Best

AA