nitinol would need a high ampage source about the size of a car battery to make it shrink a substatial amount (that would not fit in the planned size of the robot). I had the idea to wrap the nitinol wire in nichrome wire (burns or heats up when eletricity is passed through it) to make the nitinol shrink because only little voltage and ampage is required.
You only need high amps if you use very wide NiTiNol wires.
The power needed to heat up your wire will be the same no matter the method!
Using a wrap around of NiChr only means that you will loose more power to the exterior, since it will have a larger part of the surface in the air, rather than toward the NiTiNol, so it will use more power and will react slower - both ways, heating and cooling.
Have you got a datasheet (or a link to it) for your wire?