If an app only connects people to hawaladars but never touches funds, does it need FCA or HMRC registration in the UK?

Frank answers the question dead-on! I would only add the following:

If you include a fee for registration and/or take a fee for enabling this transaction, then you would be required to register with the FCA / HMRC (IMHO) as you’ve just executed a function of an intermediary. There is a false sense that an intermediary has to have/channel the funds (i.e. touch the money) in order to be a money transmitter. Not necessarily always. As you are aiding the transaction, the regulator can come to you after intent, id est you are mimicking to being a money transfer agency without licensing.

Needless to say, you are also adding an additional review because of how AML/KYC screening is done on the users of the app.