You have two options:
1. VOX -- which is tempting, until you realize that the first syllable of every phrase will be distorted. I didn't want to believe that, only realized the truth after monitoring my own signal.
2. hand switch, or foot switch.
The most elegant foot switch (IMHO) is a small digital-piano sustain pedal, like this:http://www.amazon.com/Casio-SP-3R-Sustain-Pedal-Keyboards/dp/B000792SBS
Similar units will be in your local music store, filed under "Guitar Stomp Box -- SPST". Or you can improvise something from a Staples "That was easy!" button -- pull out the electronics, keep the switch. [That was written-up in QST a while ago.]
Hand switches can be an SPST pushbutton, mounted in a piece of PVC pipe for easy holding and thumb operation. Bob Heil makes one labelled "ergonomic" with a fancier handle.
Using "non-ham" gear, for ham radio, is perfectly acceptable. My headphones are Sennheiser HD280 ("studio monitor" phones), my mic is an Audio Technica cardioid dynamic vocal mic. My compressor/EQ (rarely used) is from Behringer, not W2IHY. They all work fine with a Yaesu FT-450.