I prefer either the Old English pronunciation, as described by Buttercup, or simply dwimmer, since that seems to be an alternate spelling of the same word.
Either way, it doesn't really matter, I suppose. Dweomer, in that form, at least, doesn't appear to have made an appearance in print between 1250 and modern fantasy novels. If it really is that old, then the Old English pronunciation is probably the best bet.
Tolkien often used the alternate dwimmer, but Tolkien was notorious for "inventing" words. Not that he actually invented them, but he took words from Old English (specifically from the Mercian dialect, actually, which lacks a lot of the dipthongs of textbook Old English) and applied linguistic triangulation to project what they would look like in modern English if they hadn't gone out of general circulation.
The methodology is sound, but it's usually used in reverse -- taking cognates from two or more different languages that are based on the same root word and triangulating what the base root word would have been.
Anyway, Tolkien used dwimmer more than once, particularly with the Rohirrim who have the words Dwimmerdene, dwimmerlaik, and a few other instances referring to something supernatural or haunted.