Hi,
I'm a big lover of anchovies. As such I would suggest two solutions:
1.- My favorite solution. I just use my hands to remove the biggest and easiest scales under running water. Some scales will always still be there, but they do not actually bother me at all. In particular, they are barely noticeable when you deep fry anchovies whole (except the head and guts, but leaving the bones and fins). I suggest you put some flour on them first, to make them crunchier and to improve presentation. I find kind of surprising to hear of big scales on anchovies, that are overall very small fish. I'm sure you know what you are talking about, but just in case, I wonder if you are not talking about sardines, that look similar, are bigger and can definitively have quite big scales.
2.- If you want to take the extra time, buy and use a tool to descale fish. In my experience, fish descalers are great for bigger, more sturdy fish, (rock fish) but tend to destroy small anchovies. Maybe you can try something softer on them, like a metallic grinder (see image).