Possible to split a secret to generate a re-encryption key (PRE)?
Something similar to what you ask, although not exactly, is the PRE scheme called Umbral. It has a reference implementation called pyUmbral. (Disclaimer: I'm the author of Umbral).

Umbral is a threshold PRE scheme, which means that re-encryption is divided among several proxies and at least certain threshold of them has to cooperate. With Umbral, the delegator can generate M-out-of-N re-encryption keys, in a way similar to Shamir's Secret Sharing. 

I think you probably can reuse some of the techniques used in Umbral to split the delegator's private key and generate re-encryption key shares from the shares of this private key, rather than Umbral's approach which consists in generating directly re-encryption key shares. Anyway, both approaches should be very similar from the perspective of the application of Shamir's Secret Sharing.

I also think these techniques can be easily adapted to pairing-based PRE schemes, such as AFGH and others.