Using solar cells to power a USB device
Current is not something you can "force" onto any electrical component (without changing voltage that is). The device being powered will DRAW as much current as it needs, as long as the power source can supply that much current. So first things first ... current is something you design into your power source as a "just in case" factor - always make sure your power supply can provide twice if not three times the amount of current your load requires. 

VOLTAGE is simply a difference in potential ... think of 2 volts as holding sledge hammer two feet above the ground and then dropping it on something ... like a kids toy maybe ... whereas 12 volts would be like holding that same hammer 12 feet above that kids toy ...

Which one is going to have more potential to affect the toy?

Yet in electricity, current isn't really a factor when it comes to damage caused by applying too much voltage to a load. Just having too much voltage can do damage - the current isn't really all that relevant since devices DRAW current as needed where as Voltage is something we force onto a component - it's something we apply deliberately knowing that too much will hurt it and too little will piss it off.  :-)

So in your case, applying 6 Volts to something that only wants 5 volts is not smart - at all!

You're better off regulating the solar produced voltage - 6V in your case, but I recommend choosing your solar panels and wiring them up in such a way that they can deliver 12 volts that you regulate down to 5.

So lets say you had two 6 volt solar panels in series and then two more sets of those in parallel ... you would be able to regulate that voltage down with a simple 5V voltage regulator (such as an L7085CV) with a few resistors and caps and you're in business. Keeping the solar provided voltage at 12 or higher gives you enough variance that you'll have more hours in the day from which you can actually draw 5 volts at the needed current.

The voltage regulator will typically consume a volt or more just for itself, but finding one that has a low internal resistance would minimize this. They also typically will only allow a certain amount of current ... but most of the common ones can sustain 1.5 amps which is well beyond what you stated you needed.

Above all, OHMS LAW needs to be your religion when pondering questions like this ... it is the light that will help you understand all of it...