Can I make this without a stand mixer? I have been making it for a client who has one and they absolutely loved it so much I had to try it and , o...

My favorite tool for mixing dough by hand is a Japanese wooden rice paddle. It's one of the tools I use most often. The handle part is short and the bowl is shallow and wide, so it's very close to an extension of my hand. With wheat dough there is a point where you want to get your hands in, but for gluten free you're not really kneading (no gluten to 'develop') and they are often more sticky than a wheat dough, so the paddle is nice. When it's almost ready, you can take the dough off with a rubber spatula or table knife, then lightly oil the paddle to finish it without sticking.

Anything you can make in a mixer can also be made by hand, it's just going to make your arms more tired, so you could use a big wooden spoon or your hands to mix.
I wouldn't recommend using a hand mixer, they work well for batters, but not so well for things that are thick. I don't like small appliances to smell like burning.
A food processor with a dough blade would work just fine if you have one.