I would feel far more secure about using the Staples service than submitting anything online, which would mean having an electronic copy out there. The folks at Staples fax a lot of stuff and they don't give a flying fig about what they're faxing that I've ever noticed. If you hand them the ready to fax item, including the cover sheet, they grab it, fax it, hand it back and charge you.
And, by the way, I would also take the time to complain to the entity that's insisting on a FAX. Very few of us ever had FAX machines and these days even fewer of us do. It's perfectly possible to send the same document via e-mail or via a secure customer portal, and in this day and age that's what they should be doing. Insisting on FAX makes customers' lives miserable for no reason.
Brian - Windows 10 Pro, 64-Bit, Version 2004, Build 19041
Always remember that computers are just glorified light bulbs - they rarely fail in continuous use and usually go pop when turned off and on.
~ Technician with the username Computer Bloke, on Technibble.com