I think you definitely need the washers tbh, they’re a bit of the rim that just happens to not be attached. I had a bit of a look at mine and I reckon it’d build without them but the amounts of metal are pretty tiny in comparison to a normal uneyeletted unwashered rim.
I do build mine with normal nipples not the squorx, mostly because wheels are so much easier to build with an adjustable depth nipple driver. IMO the squorx nipples are 100% designed to be more convenient for wheel building factories, not with any thought for us. Sapim brass are pretty much the same shape as squorx where it goes through the washer so I use those, never had any isses with the wheels I’ve built that way, tbh I suspect any nipple would work just fine but it does feel nicer to use one that’s a similar shape
(as ever, I weigh nowt so do take that into account but they do get used reasonably hard so if there was a fundamental issue I’m pretty sure it’d have shown up by now. But they’ve been great- the rims are superb tbh and the nipples just seem to fit as well as anything does)