createrawtransaction online createrawtransaction is a bitcoin-cli command that generates a raw transaction given one ore more transaction ids and a list of Outputs, which are the destination amounts that will receive the funds.

AFAIK, The raw transaction is only based on the blockchain, and does not require any private key or address; the signing process is done separately, using signrawtransaction.

If the createrawtransaction process requires no secret keys, is there a way to generate a raw transaction online, using a web service?
That's correct, a private key is not required to use createrawtransaction. The private key is only required during the signing process of signrawtransaction just as you stated in your question.  

If you are looking for a web service that will allow you to create a raw transaction online, I suggest you check out http://coinb.in it does exactly this, as well as broadcast the transaction, and allow you to save a local copy to sign the transaction offline.