I believe it should be possible. A composite, with Sugru as the matrix, and a suitable non-Newtonian fluid as the dispersed phase. Now, what fluid to use… Most likely something with long molecular chains with significant but weak-ish mutual interactions. Starch is a common one for demos, maybe high molecular weight polyethyleneoxide could work too? (short google search says apparently yes… but what’s what the pros use?)
Edit: Some other classical mixture in use is polyethyleneglycol with suspended silica nanoparticles (I saw 120 nm sized ones).