I find it heartening what lively response there was to this idea. I'm cheering you on too, the sitar has a very interesting effect on people, it's other worldly.
It's certainly possible to get the vibration sound, I've done it accidentally on both my guitar (steel string) and Uke (Aquila Nylgut strings).
But, I'm not sure "how much" you want it to sound like a sitar: the note bending on a sitar comes from the very high frets, much like a Chinese Pipa.
See photo
Not that this would be a complete road block - depending on how heavily you are willing to mod the Uke, you could raise (replace) the nut, and there would be multiple ways to make high frets like this. Either by copying the sitar (using metal arcs) or simply stacking layers of narrow shims on the frets with some kind of adhesive. These shims could be made of bamboo slats, which are very hard due to high silica content, which would mean the strings would vibrate freely, and bamboo is easy to split into narrow pieces, it separates easily.
For the strings to sound right:
The harder the strings, the easier it is, the sitar uses metal strings. Aquila isn't the hardest Nylon out there, and there are steel strings for Ukes, but AFAIK only for the wound 3rd and 4th strings. When I tried Ko'Olau Golds (nylon), they sounded harder to my hearing than Aquila Nylguts (more guitar like).
Chinese pipa strings are very hard and guitar like - available on ebay - would likely need a new nut to accomodate the wider string diameter. The silk sounds more soulful than metal, and operate at lower tension than metal (Ukes can't handle high tension required for unwound metal AFAIK).
Good luck, keep us posted!
Yes!
