The product owner handed you a prototype; hand him back better ones (until you are done)
It sounds like you’ve been provided a paper prototype to start off the project. That’s not a terrible beginning. I suggest you communicate back to the business owner in the same language, by providing progressively capable prototypes.
Your prototypes should start with paper, move onto digital mockups, and then get built with “real” technologies.
Treehouse has an excellent guide for this, which concludes:
The wonderful thing about prototyping with a framework is that the prototype often just becomes the real site because the structure and styling are already in place. There’s no need to recreate the site from scratch if it’s going to use the same framework.
You may wish to provide a formal specification as well, especially if you remain worried about getting blamed for a bad result. But you will probably get more feedback from the prototypes.
Meet your deadline
Note that your later efforts will not be classical "prototypes" as all, as they will not be disposable (or parts of them won't be). The last, most capable, iteration you complete before deadline becomes your deliverable.
Your deadline is the best-defined requirement you have. Have something complete and coherent that you can deliver on time.
Collaborate with your testers
If this loose process is a new thing for your company, your testers are probably even more at a loss than you are, and may be looking to you for guidance. You’ve got to get some of their time early in the process. Let their boss know you are trying to help them provide a meaningful test without receiving formal acceptance criteria.
Find out if the testers have anything firm they need to provide, like proof-of-testing documentation, which you can “back into.”
Try Test First Design
Since you have no formal requirements, getting test cases to develop towards would provide some structure.
Get yourself a passing familiarity with Test First Design and/or test driven development and provide guidance to your testers on the process as needed. For a quick project like this, you don’t need to become expert at the process. But using a proven methodology will reflect well on you and your testers.
Stick to standards, especially for UI
You don't have requirements about look and feel, but you do have a deadline. Use somebody else's design work to minimize the work you need to do to create a professional looking artifact.
Choose a standard UI for your site and don’t customize it unless/until directed to. I don’t know what platform you are developing for, but Bootstrap or Google Material Design are two examples.
Communicate, but don’t pester
I would suggest sending one email to the product owner a day. Only send more than that if it’s an emergency.
If you have questions, describe how you will proceed if you don’t receive guidance. For example:
Will the users of this app need to access it with mobile devices? Right now we are assuming this will be a desktop/laptop only system.
I’ve been involved lots of projects for folks who didn’t know the term “requirement.” Most were successful. Hands-off product owners give you the latitude to build great solutions.
Note, some project owners in these projects were impossible to please and hid behind the “I’m too busy to...” excuse for their incompetence. But most were “delighted” with the end results.