I wouldn't recommend cheap wireless mics as my experience with them is not good. Many are plagued with rogue AF artefacts/noise and RF performance problems (e.g. drop outs). The low-cost DJ wireless mics are generally for guys that are standing a few metres away from their equipment at most - but I haven't got any real world experience of the Numark setup so it could be that knight in shining armour that you are looking for.
I'd want to test out that Numark mic before making any commitment to it - and also be wary of any product that you buy in fixed frequencies... worst case is if the channel you have bought is prone to interference at the venue, you are stuffed. As for recommendations, I would also check out the Alto offering (Radius 100) and also the Line6 XD-V35 if you can find one closer to your budget.
What I would really recommend though, is a used Sennheiser EW100/EW300 setup through eBay, probably a G1 for your budget (this is the proper stuff for the pro/sumer market) - but even then you are going to be lucky to get it anywhere near your budget... but you never know, I have witnessed some radio mic bargains go through eBay. Remember, you could buy a plug in transmitter for your existing mic and a receiver, or a mic and a receiver.
EDIT: this just went on eBay - [url="http://www.ebay.co.uk/itm/Sennheiser-Radio-Mic-/141929523981"]http://www.ebay.co.u...c-/141929523981[/url]
Good luck!