It seems to me that
1. Whether the ESI/ PF contributions are paid in the contractor's or the principal employer's code, the ultimate responsibility is always with the principle employer.
2. As long as there is a genuine contract between the principal employer and the contractor (and atleast principal employer registered under Contract ...Act, wages are paid by contractor etc.), labour enforcement authorities should not mind contributions of contractor's labour submitted in principal employer's code.
3. As employer you might have every right to demand the contractor to obtain registration. Of course, I have heard that at times the authorities are not be keen to register a contractor unless he/ she has more than the minimum requisite number of workmen engaged under him (because they might want to keep the onus deliberately on principal employer for justifiable reasons). Therefore what this means is that you might have to work with larger contractors, if available, who are having a sizable number of workmen and therefore, have their own codes.
Though for a young manager like me, contract labour and related matters still seem to have many areas of greyness, above is what I feel. As always, there can be no substitute for a considered labour law consultant's views, or better still, go for word from the horse's (enforcement authority's) mouth if possible.
best wishes