Just now seeing your question.
I *think* you are wanting a material that you can create an impression in (like handprint or footprint) then harden, and not
to later use that hardened impression as a mold to cast some other material in.
If that's the case people often use polymer clay
, and for that purpose most often they'll use the brand/line of it called original plain Sculpey
(which comes in a box) --mostly because it's cheap and white.
The kits you'll see for doing that at home usually use Sculpey, but include a frame to put the clay in, etc. (you can use a frame of your own). Because that particular line of polymer clay is somewhat brittle after hardening (in the oven) when thin, baked slabs of it could be broken if stressed much so best to put the clay on the backing in a frame or on something else like a plaque/etc to give it more strength and protect it from getting stressed.
Polymer clay doesn't have to be mixed with anything, and it will never harden until it's heated sufficiently (unlike air-dry clays).
Also polymer clay will take and hold details much better than most air-dry clays, although the softest polymer clays will sometimes not create or hold those details as well as the regular brands/lines (like Premo, Kato Polyclay, FimoClassic, and Cernit--sometimes FimoSoft is okay).
You can read more about making those handprint/etc things, if that's what you're asking about, in my previous answers (at YahooAnswers--I'm Diane B.
And you can read about the "kinds" of clay there are these days here too:http://answers.yahoo.com/question/index?qid=20100621051506AA53JtD
(ignore the 2nd paragraph)
As for sensitive skin, that might depend on just what you mean by sensitive --a normal baby?, a person with many allergies?, etc. A few people may react to raw polymer clay; if that's the case, they'll usually try a barrier cream and then gloves of some kind (if they're allergic to latex, there are others). You can read all about those things on this page of my site:http://glassattic.com/polymer/safety_health_cleaning.htm
(click on Rashes & Allergic Reactions)
(Normal babies and kids would be fine for doing the handprints though. Just wash their hands afterward--and before they can put them in their mouths though not "toxic" even then.)
If you don't want to use polymer clay, some air-dry clays will be better quality than others (e.g., Creative Paperclay), and even some grain-based homemade clays should do well enough though all air-dry clays will shrink a bit while drying--like salt dough clay (...and btw purchased Play Doh isn't grain-based, though some homemade "play doughs" are).
If those don't answer your questions, ask here again with more detail and I'll try to remember to check.