Using synthetic won't hurt anything and is recommended for all seadoo 787-951 engines. Make sure it is only API-TC rated. Castor is not correctly rated and shouldn't be used on powervalved watercraft. The castor being a bean oil will also absorb moisture which is bad and there is no need for the super high film strength in castor in a stock ski especially at break in. If this is a 787 you still have to supply oil to the rotary gear even on pre-mix.
So no. don't use castor.