You've said tradesman, I'm assuming construction/ building work here. It gets messy with construction and there are potentially bigger issues than HMRC for the contractor, the 'sub-contractor' and or the end client, depending on what work is undertaken by the 'sub-contracting' person.
(There is a specific category and scheme for actual sub-contraction CIS but they need to be registered under it.)
The words "it would be more like a subcontractor" are a huge alarm bell.
Otherwise, a genuinely self employed builder (A) with their own customer base can go and do work for another genuinely self employed builder, (B) but they wouldn't be getting a wage from B, they (A) would invoice B for the work/services/equipment supplied. (and it would be very unlikely to be weekly) They would be very foolish not to have a contract clearly stating what they were contracted to do.
In order to remain considered self employed, amongst other things A would need a number of other customers. If they aren't already self employed, just walk away now.
From the POV of the person B is constructing for, any mistakes/ issues with A or their work will generally be down to (and possibly disputed by) B's insurance unless there is a contract between B and their client, saying otherwise. B then pursues A through the courts for recompense.
A real subcontractor has a contract with the contractor for the services they provide.
An employee of the contractor cannot also be a subcontractor.
If the 'subcontractor' is later found by HMRC to be an employee, and there are later issues with the work or time frame, the contractor is going to be well up the Swanee.
If they do it anyway, A would be well advised to have their own injury insurance.
B sounds at best clueless, and at worst dangerous for A, and possibly B's clients.