Ok, I can work with that I think. I'm not much of an iPad person, Android's a little easier to navigate for sharing (IMO). Printing would be the easiest but I'm spoiled, I have a wireless printer that I can send stuff to from my phone or tablet. In my case if I didn't have access to my laptop, I'd print the PDF from my tablet, handwrite it all, then take a picture of it with the tablet camera. I'd use the photo app to crop it down to just the paper edges, if needed. Then there should be a Share option in the photo app and I'd pick email from there. Then it'll be added as an attachment to the email and I'd send it off to dispatch.
If you can't print it, that gets a little more complex. The PDF I downloaded doesn't have form fields so I'm not sure an easy way to fill it out on a tablet. But mobile apps sometimes have more features so you could try the Adobe Reader app and see if you can write on the document through that. There used to be an option to add notes with that one I think. Then once you save it you can either share it to email or maybe you can add it as an attachment through the email app.
I don't know if they're still around but there used to be print apps that would let you print to a public printer. Like send it to FedEx print shop and pick it up from there. Probably overkill for a single page though