What is the maximum physical current that can pass through a standard USB cable?
In July 2012, the USB Promoters Group announced the USB Power Delivery ("PD") specification, an extension that makes use of certified "PD aware" USB cables with standard USB type A and B connectors to deliver up to 2A @ 5v.

In addition to the type A and B cables, the power delivery option will also be part of the new USB-C standard with the reversible connector (like Apple Lightning).

So theoretically you would need to get hold of one of these special PD cables to safely pass 2.1A.  Before this, the maximum you could send over a standard USB cable for battery charging was 1.5A @ 5v (and devices not being charged were limited to 100 mA or 500 mA).

The gotcha is I can't find any of these PD-aware cables available for sale.

Standard USB cables use really small wires.  Most use 28/28 gauge, meaning 28 gauge for data and 28 gauge for power, because they are designed to handle only 500 mA.  28 gauge is tiny.

Better cables use 28 gauge for data and 24 gauge for power (which is still pretty small).  You can search for these using "USB 28/24" in Amazon (without the quotes of course).  The same article linked to above claims USB cables with 24 gauge wires can handle 2A, even though that's above the official USB spec of 1.5A.  Although come to think of it, I believe a lot of tablets can draw up to 2A when charging.

24 gauge cable has a resistance of 0.0257 Ω/foot, while the resistance of 28 gauge cable is a little over 2.5 times as much.  So 2A through a 24 gauge 6-foot cable will drop the voltage 0.3v.  Not great, but okay.  The same current through a 28 gauge 6-foot cable will drop the voltage 0.77v -- not good.

So it looks like you are probably safe to use a standard USB cable, as long as it is not too long and uses 24 gauge or larger wires.