I tend to use Blu Tack because it's quick and easy, but it's not always very robust. Anything similar is going to have plasticers in it, either oil-based or something like glycerin. A spot of silicone sealant might be an alternative, though it could be harder to remove without damaging your delicate work. (Maybe gently heating with hot air would help.)
I sometime use tape as well, and find good quality paper masking tape works better than PVC tapes as it contours more easily.
For a firmer support you could try polycaprolactone, which is widely available on ebay as a modeling material. (Try searching for "morphplast", "plastimorph", "polymorph" etc.) It melts in hot water or with hot air and can be easily moulded into complex shapes, then it sets hard in a couple of minutes. (Also easy to file for finishing touches, and fully reusable.) It's not sticky so needs to be taped down, but you can quickly form custom jigs with it for holding awkward items.