It would be useful to know what kind of PET scan is planned for 19th April - it may just be a choline PET scan which is significantly cheaper and unlikely to be cancelled due to production issues. Alternatively, it could be an Axumin scan which is cheaper that PSMA and available at more private centres but more expensive than choline.
In reality, with the long Easter weekend next week, I would be surprised in you could get a PET scan earlier that 19th April, even if you pay.