Rob - I developed a hyperhidrosis problem earlier this year, hasn't gone away.
Go to the pharmacy and try roll-on over the counter stuff, usually containing aluminium chloride I believe. The one I use is called Driclor. Initially you need to use it daily (before bed), and take it easy because it really, really stings at first. After a while you can taper your use, I only apply it twice a week now.
No underarm sweat at all, even at the gym, which is a little freaky. Hasn't caused any temperature regulation problems just yet, although applying it all over someone might be an interestingly nasty way of offing them - either the stinging or the inability to sweat.
No problems with staining clothes either, apply it at night after a wash and let it dry before clothing up or getting into bed.