Asking for bank transfer in 2023 post Covid with the bank and govt pushing less cash transaction isn't suspicious in itself. I take bank transfer, since I require a deposit and don't accept vouchers.
And nothing is suspicious in someone offering cash after informing them you don't accept transfer lol. What else do you want them to offer? haha
The important thing is ensure if you're accepting it, you check your account on your phone that the payment is received, NOT their phone. I would say is even best if you have an account with one of the App banks as opposed to the high street ones, as they all have transaction notifications and are instant. There's literally no waiting for transfer to reach you, is instant.
A tip I would add to mitigate any possible "charge back" is to confirm rate and service in writing over text, but without stating anything explicit (X rated) regarding service. For example, say after you've confirmed you're booking them on the phone, if that how you work, follow it up with a text saying something like, Hi John, your appointment is at 2pm and your fee is £4. Here's my bank details for payment, and whatever else is important. Also, maybe after their appointment, send a thank you for your patronage and see you next time message.
If anything happens you have that to show bank that the payment was intentional.
I hope this is helpful and not compounded your fear