Cheryl, to me (as I can't speak for others), white chocolate doesn't taste at all 'chocolaty' but just has the mellow rich flavour of the bean's fat and the cream used in making it. Even if someone added a very small amount of expresso or coffee liquor to it, it would only taste like coffee, although fairly faint. Not at all like mocha.
White rum has little flavour so I'm assuming you mean dark rum. I think dark rum would overpower it but perhaps not one that's somewhere between the two. I don't know if Captain Morgan makes one. If you like the flavour rum adds, use it. But Captain Morgan is a very rough tasting rum so yes, cut it down to 1/4 cup or less. Make up the difference with cream when cooking the egg yolk mixture.
It seems like there are a number of Julia Child Chocolate Mousse recipes and not all are the same. The original recipe published from her cookbook in 1961 has this for the ingredients.
4 egg yolks
¼ cup instant sugar (very finely granulated)
¼ cup orange liqueur
6 ounces or squares semisweet baking chocolate
4 Tb strong coffee
6 ounces or 1 ½ sticks softened unsalted butter
¼ cup finely diced, glazed orange peel (optional)
4 egg whites
pinch of salt
1 Tb granulated sugar
Does this sound the same?
Orange liqueur like Cointreau sounds lovely with white chocolate but perhaps not what you're aiming? How does a little Grand Marnier? It has an orange flavour too but quite different to me. It's more robust than Cointreau so I wouldn't use that much. Ultimately, it comes down to your preferences and any guests you're serving it to. (As a side thought, I wonder how a nice brandy would go with white chocolate mousse? I've used it in different desserts before but back when I could afford to stock my cooking pantry with some liqueurs, rum and brandy.)