I've never made eggnog, but lately I'm starting to learn to make other things with eggs, such as mayonnaise and lemon curd.
You can buy pasteurized eggs at the grocery store, and some people claim you can pasteurize eggs at home (though the USDA says otherwise). In that case the eggs and milk would be pasteurized, but the eggnog itself would be uncooked.
Interesting to consider that bit about the USDA and home pasteurizing eggs. I do a lot of ice cream/frozen custard style things and have used raw yolks before after using low temperature cooking via immersion circulator to "pasteurize" them first. I usually refer to Douglas Baldwin for a majority of this stuff.
http://www.douglasbaldwin.com/sous-vide.html
Though the first article that popped up on the search has some good reading on it from what I'm seeing. https://www.streetsmartkitchen.com/how-to-pasteurize-eggs-so...
Not the person you asked, but you can make mayo with a bender or a whisk. Emulsions like mayo or (no-egg) aioli are tricky until you learn to see how they behave, and after that are pretty easy.
You can buy pasteurized eggs at the grocery store, and some people claim you can pasteurize eggs at home (though the USDA says otherwise). In that case the eggs and milk would be pasteurized, but the eggnog itself would be uncooked.