Castor sugar is simply sugar that is more finely ground than granulated sugar. I would think the only reason to use it is that it will simply dissolve more quickly. I use regular sugar in mine with no problem. Sometimes when I want sugar to dissolve more easily (making caramel, especially), I just whir my sugar in the food processor (or mini prep or coffee grinder) for a few minutes, and it works great!
It will also dissolve more easily if you combine the sugar and water and then cover it (so water doesn’t evaporate) and let it sit for a couple of hours. When I make caramel, I do this (and whir the sugar), and the sitting gives the dissolving a head start.
And what delicious cake will you be syruping???