you can, just don't expect it to be widely adopted. plus your niche shouldn't have security and usability concerns.
also, be aware that applet support isn't likely to last much longer. several plugins aren't supported anymore on the desktop, and there aren't any at all for mobile devices or tablets. since java 1.7ish even running signed privileged applets on supported browsers on desktop is a pain. in short: maintaining applet support is problematic and nobody seems to bother anymore, specially since there is no benefit: js can now handle most of what applets did in the browser in the past, right out of the box and better.
there still are a few very specific usecases for applets like, for example, to access smartcard readers from a webapp. but even then, applet maintenance and deployment is hardly optimal and you'd probably will end up ditching the whole idea and lookig for a workaround.
and of course you don't have to learn "every language out there" if you don't want. however, if you want to do stuff for the web today (that's what applets were for) you simply won't get away without learning js. it's not optional.