To my mind, there's two scenarios here.
One is charging directly from solar, and I doubt anything you can hold in your hand has the capacity to do that, even given, at best, 10 hours of sunlight. You need an output of around 4.2v and around 500mA to 750mA (what my charger puts out)
The other is charging a "holding" cell from solar. Once that's topped off, you can recharge an ecig battery from that using your normal charger and an inverter (changes the battery's DC current to AC current that your charger likes). I haven't conducted a field test, so I have no idea how long it would take to charge a 12 battery from a "drained" condition (12v batteries should never be drained below 10v). I would expect hours at a minimum, maybe even a full day in ideal conditions.
A 12v battery, going thru an inverter, to power your normal ecig battery charger, could easily handle it. But I'd guess a small solar charger would have to be recharged several times or run for a few days just to recharge one ecig battery.
I'm using the same approach as Alice noted above, I can charge my ecig batteries using the car if I have too, but you can't have too many already charged (I keep 9 18650's charged at all times). My solar panels are really for lights, TV, etc. If we were without power, I doubt I'd divert any of that mission critical energy for ecigs.