I can imagine that if you "implemented your own browser" (or included a browser with redirect hooks)... you could request Etsy's oauth page, have them log in, let them approve the scopes and allow access, and intercept the redirect to a website and instead capture the token information for your app.
You would still need to give a website name to Etsy to approve your redirect URLs, but this entire process should work.
FYI: by "implement your own browser", I mean do a GET request to a url (with cookie support), parse the relevant info you get from Etsy's servers, and display the important information to your user. You wouldn't need to fully support all HTML, just support reading the important text and links you get from Etsy.
I don't know if this is at all against Etsy's Terms of Service. If you are considering such an option, I would suggest looking into whether this process is OK or not. Maybe even confirm with an Etsy developer.
That all said, I think it's pretty clear Etsy's v3 API was not designed for a product or service without a website.