QOFE
I am really at a loss to think of what legal protections trans people enjoy or would enjoy that grants them permission to jack off in the park. Do women have this right? Not that i'm aware of.
How would he benefit by self ID'ing as a woman. He could walk into a woman's toilet, same as now, there is no magic force field. Self ID wont grant him access or licence to commit sex crimes in the ladies, in the park or anywhere.
There is absolutely no benefit to him to self ID as a woman, there are however a huge number of obstacles to life if he were to self ID as per proposed changes and not actually live his life in that role. It is incredibly hard to live with ID documents that don't match your presentation or third party perceived gender. This is all backed up by the evidence of the countries that have self ID.
If he actually does self ID'd would his crime go down as part of female statistics, there is a chance, but then there is a higher chance that during the prosecution his self ID will be picked apart and he would also face the charge of fraud on top of his sex crimes.
Self ID is not a get out of jail free card for sex offences.