Of course, it is impossible by using the universal and commonly used methods. I think/wish you are entirely and clearly aware of the scale you have mentioned about and more importantly "the huge gap between the size of nanowire and those of mechanical test instruments (even in micro scale)".
BUT, (!?) you can search for applicability of some rarely-used approaches e.g. single fiber pull-out test by AFM (probably not applicable for nanofibers ?)...
In my opinion, using some computational methods without experimenting or micro-mechanical testing attempts with classical methods by regarding many assumptions could be performed.
Recently, we performed creep and stress relaxation tests on collagen fibrils (diameter ~100 nm and length ~30 μm), using MEMS devices, a real time edge detection algorithm, and a closed-loop PID controller. The work can be found in the following link:
The diameter of your nanowires are an order of magnitude smaller, and therefore, will be harder to manipulate. However, MEMS based techniques with feedback control is definitely a way to perform these tests.