You can send them a suitelet that is available without login that lets them do whatever and then the suitelet's backend can handle the quote -> sales order process.

Wouldn't they have to be logged in, in order to actually process the quote? To clarify, we don't currently have customer centers enabled.

No, they don't have to be. If you make the suitelet "available without login". Then they can view the Quote (without being logged in) and just press a submit button. Then the backend of the suitelet can convert the Quote to a Sales Order.

Ok, will give it a shot, thank you.

But you should add some of your own basic security. Otherwise it will be too easy for one customer to view and process another customers order

Good point, thanks!