OP, you have 3 questions that need to be dealt with: sex discrimination, gender reassignment discrimination, disabled access.
Looking at them separately, and bearing in mind you don't have time or budget for renovations.
Disabled access must be available to both sexes. Only one loo has it. Therefore loo 1 is already mixed sex.
Sex discrimination. You have 1 mixed sex loo and 1 other loo. If that other loo is men only, you are giving the men more facilities than women. That's not allowed, so loo 2 has to be mixed sex as well.
Does loo 2 meet the requirements for a mixed sex loo? If the cubicle and urinal can be used separately at the same time, then it is not single occupancy. So it cannot legally be mixed sex.
To meet the requirements it must be a single occupancy room. This requirement can be met by adding a lock to the outside door, so it is used by only 1 person at a time. As it will be used by women, it also needs a sanitary bin. That should be possible even without a renovation budget.
Finally, if you have 2 mixed sex loos, do all people with the PC of gender reassignment have somewhere they can use? The default is they use the provision for their sex. There are 2 single-occupancy mixed-sex loos. They can use either. No discrimination. The fact there is a urinal in there is irrelevant, because it is now single occupancy so nobody will be using the urinal when they are in there. It has no more relevance than whether or not there's an aspidistra.
The only legal solution, within your constraints: add a sanitary bin and external door lock to the gents, make both mixed sex, single occupancy.
Hypothetical. If both units were accessible, so disabled people could use either, you could have 2 single-sex accessible loos. In this case all trans people would use the facility for their sex. The Supreme Court decision pointed out that women who pass as men could sometimes be excluded from female provision if their presence would cause alarm or distress to female users (clause 28). But the female loo would be single occupancy, so a transman wouldn't be using it at the same time as another woman, wouldn't cause distress, not excluded, no need for separate provision.