The Quickie power supply is 36V coming from the batteries. The output capacitor will not see all of that for more than a second or 5 seconds. Nothing higher is necessary.
But, the better film caps start around 200V. Some are only available with a 600V rating.
Just be aware how much larger film will be and use the lead length to your advantage.
Thanks, Grainger49! So I was guessing that the lower the voltage rating the thinner the dielectric, and the thinner the dielectric the better it sounds. It's good to know I can try out some of the fancy caps!