The product is a bracelet with some custom sensors and a bluetooth transmitter, connecting it to a smartphone. I have a bulky working prototype, not wearable, that has to be minified.
I'm a software developer with no experience in hardware development whatsoever.
Depends on how connected you are, but what I would do in your place would be to simply ask around my network of friends or old coworkers for a mechanical engineer and a hardware engineer (that's pretty much the minimal team you need).
Basically, find some friends and develop this together. I would not recommend you outsource a prototype. You'll spend oodles and oodles of money on simply trying to get your idea across to people working for money on multiple projects.
What you really want is a few people so enthusiastic about your product that they'll want to develop it because they are passionate about it and think it is cool. You compensate them generously (for instance, by offering them appropriate compensation or equity in your company/business), and work together and launch your business together.
Or you could go the route of trying to outsource everything but spend several years trying to get a product to your spec just in the back and forth and clarifying misunderstandings with the money that goes with it. By the time you get it out ready for sale it might not even be a cool product anymore or such a hot seller. The only way I'd go this route is if I had already done all the design work and only needed someone to build it for me and if it could be done in the span of a few months.
But if you can find people in your network that you can actually talk to, it would be much simpler.
You're a software guy, don't you know any HW and MechE friends from university or previous jobs you could contact?