I'm a UX strategy consultant with significant experience working with developers and startups. In most cases, yes, you should hire a UX designer first.
In my ebook, I’ve written several reasons each for hiring a UX designer first and for hiring a developer first. Here are the ones which apply to what you are describing.
The case for hiring a UX person first:
1. They can help you validate or create the requirements for your product. They do rigorous research, focused on how your potential users would use your product - as opposed to a market researcher’s research, which focuses on what they will buy.
2. UX designers are good at imagining the world as it can be (as opposed to the world as it is), based on your users’ goals. So that helps you to truly move ahead of your competition.
3. A UX designer can build a prototype that helps you raise funding without requiring any code to be written. You don’t need to write code in order to have an MVP. Even a fake door pretotype (not prototype) can gauge interest in a new product or feature.
4. This is rarer in the mobile app world, but for website projects, companies may have already decided on a no-code platform.
The case for hiring a developer first:
1. You may have a solution to a complex enough problem that just getting a functional prototype built will be a huge win. This may be a good path for getting your first check from a big customer.
2. You may have already committed to a ship date and “can only get it built”. A UX designer works most effectively when there is time upfront for user research. If you need someone to jump straight into design and development, you may have to live and learn.
3. If you yourself have both deep expertise in UX - as opposed to just knowing how to use a prototyping tool - and the time to do UX work, you may be able to just hire a developer.
I know you already have a wireframe, but you should expect your wireframes to change after working with a UX designer. UX (as opposed to visual design, often called UI/UX) is more focused on problem-solving and research than on making an existing wireframe pretty.
Work at a fixed price rather than hourly if you are concerned about going over budget. Expect UX consultants to charge per project phase and/or per iteration to work well within this framework since a big part of their work is discovery. Fixed prices are a better arrangement for both client and consultant because it moves both of you away from micromanaging the work process and scrutinizing timesheets.
Let me know if you're interested in a call to discuss further.