TKinter is the GUI part of the Python standard library. Every installation of Python should include tkinter.
So your script should just run on any platform that supports/runs Python. As long as Python is available to install on the iPad, you should be good to go. But I really don't know anything about the iPad. We are a Linux forum, not a Windows or Mac forum.
If you can't install Python on the iPad, perhaps you should look into borrowing, or acquiring a laptop, running either Windows, mac or Linux. You shouldn't need anything too flashy. As long as you can install and run your Python application on it, you should be good to go.
If that's not a viable option, you could try contacting the organisers of the competition. Explain that you only have a clunky desktop PC and you don't have a laptop available. And ask if they will have any PC's/laptops available for you to use for your presentation, with Python pre-installed. That way you might just need to bring your script/application on a USB stick. Which might be even more convenient!