I've recently been through a tenant dispute, using the deposit schemes.
These schemes are very much of the view that the deposit belongs to the tenant & you must provide a watertight case in order to make deductions from it.
Despite my ex-tenant leaving the place filthy & having photographic evidence of this, plus photos at check-in & a signed, dated inventory showing he inherited it in clean condition, the deposit scheme found in his favour.
I had to pay for it to be professionally cleaned at my own expense, which I had receipt for & needed to get done before the new tenants moved in.
The process took about 6 weeks (see timescales on the deposit schemes website).
I wouldn't hold out much hope of getting anything back, as it will be difficult to prove beyond "reasonable wear & tear".
I take it you have close-up photos of the floors & walls, at check in/out, which are embedded in an inventory & date-stamped? And the the tenant has initialled every page of the inventory, as well as signing & dating the final page? These are the technicalities which got my tenant off the hook.
Good luck, but I would think very carefully before proceeding.