3c 10 ah. NO. If you really want the max lifespan out of any chemistry, you cannot run it at max continuous c rate. Get the 15 ah battery, if not the 20 if that is a big amp controller. If it's reallly high amp, you'd be stupid to even buy a ping. You need headways, A123, A big stack of konions, lipo.. etc.
That controller has quite a long row of fets. I bet it's bigger than a 25 amp. Do you have any kind of battery now? If so, you can test the actual amps that controller puts out using a 5 buck automotive amp meter from harbor freight.
On the other hand, 22 amp infineon controllers are going cheap on the for sale page.

One of those should work fine with a 3c, 10 ah ping.
Good on ya Kiwi, for getting good use out of your pack. Clearly you have nothing but perfect cells in your pack. But there is no certainty that will be the case for everybody.
How many cycles, or miles? 500 cycles, 5000 miles yet? That would be acceptable to most people, even if it's half what a ping could do when loaded closer to 1c. Personally, I consider 1.5c the max rate for a 2c ping expected to last a long long time. So 15 ah can do a 22 amp controller, even if it's climbing a hill 15 miles long. Most people don't strain a battery that hard, but it's suprising how much damage a route with lots of stop signs can do. A lot depends on the rider, so my advice always assumes the worst possible conditions.
I think of it this way. How many cells paralelled in a 10 ah. two. What's the c rate if just one is a weakling. It doubles. With a 15 ah pack, on weakling is still bad, but not as bad as when you cut the pack size in half. One weak cell, and you are discharging a 10 ah battery at 10c with a 50 amp controller. Ouch! So with the bigger pack, the weak cell may never get enough stress to fail, while with a small pack it does.
If you want to be really light, then forget the ping and go straight to hobby king for 30c lipo. Then you can do a 5 ah pack.