An alternative, which was suggested above by HiHo Silver, is a wired headset mic. Most headset mics which can be used with a wireless system can also be used with a cable... though some sort of adaptor may be required (especially if your mixer doesn't have 'phantom power').

There are plenty of small mixers available these days (Behringer have quite an extensive range, though the models change each time the CEO changes his socks!). Such mixers can quite easily be mounted on a microphone stand or small table, and you could plug both your guitar and headset mic into that, sending the mix to a channel on your main mixer, or directly to a slave amp or self-powered speakers.

That will give you fairly easy control over the output - and will provide the 'phantom' for a cable headset.

This approach is cheaper than a good radio system, and also eliminates the need for batteries - it's also handy for home recording into a PC or MiniDisk recorder.