There is nothing says you have to take the first money offered to you (even if you can work out the deal, legal, etc). You should talk to other angels/VCs who

There is nothing says you have to take the first money offered to you (even if you can work out the deal, legal, etc). You should talk to other angels/VCs who may have more relevant expertise. Alluding to the fact that you have a legitimate interested investor may also make you more attractive to these other investors and get them to move quicker. Or folks more experienced in angel/VC investing may co-invest with your existing interested party. This may also help ensure that everything is on the up and up.