Yes to both questions. It's probably a code violation so use this idea at your own risk: File the fat blade of the plug down until it fits the non-polarized outlet. Using a polarized plug on a non-polarized device like your motor won't hurt anything. The other way around might.
I did a quick search. You can still buy non-polarized plugs online. You might be able to get them at a better hardware or electrical supply store too.
I used "buy non-polarized plug" for my search.
Here's one example.
https://www.google.com/search?q=non-...49504528767866
Cheap and it looks better than many replacement ends. black ones are available too.
Rodney