A credit default swap is an insurance contract. It is not a tradeable asset.
The premium leg consists of those contracted premium payments that are made to the CDS issuer. If by trading this leg separately you mean selling the right to pay premiums, then obviously no-one is going to buy the right to make premium payments without the right to make a claim in the case of a default. Why would anyone pay to make future payments with no benefits?
The default leg consists of the contracted benefits the holder of the CDS will receive in the case of a default. While the issuer of the CDS may be able to offload some of their risk of a claim through a re-insurance transaction, this is not an option for the CDS holder. The idea of the holder of a CDS selling their right to receive payment in the case of a default is a non-starter since there would be no profit to be made, only the additional expense of entering into a legal contract with a third party. The holder of the CDS is legally obliged to pay the premiums and legally entitled to the associated benefits. On top of this, there would be the legal and administrative costs of trading.
So the answer to your question is "no". There is currently no such market, and unlike the "stripped bonds" market, there is no conceivable circumstance under which such a market would be feasible.