"If you really want to go cheap, try this, possibly backed by this pre-amp."

Any contact mic is a spectacularly terrible way to mic a melodeon. It does ALL the wrong things: it gets a horrid ringing noise from the reeds vibrating and all the key clack noise, and none of the normal sound you want to hear. It might work on a guitar, but it's useless on wind instruments, which is what a melodeon is, for miking purposes.

There are similar piezo microphone units that would work, or some piezo sounders that work in reverse as a mic, but don't use anything designed as a contact mic.

Also piezos need a high impedance input - many guitar amplifiers are suitable, or a preamp designed for piezo transducers. In general it won't sound good (thin and screechy, no bass) plugged into a mixer mic channel.