You might be able to use a needle-top bottle to fill through the wick holes. There's a top cap that unscrews, and then there's another top below that, that unscrews. I just unscrew the top a little, crack it open so the wicks don't fall out, and fill with a normal bottle.
I'm using a blunt needle tipped bottle(s) to fill it, fwiw. Easy to do through any one of the wick holes.
I've also not had any leaks, but I do keep it upright most of the time, either in my front left pocket or on a desk.