Just going to mention, for those who can't afford a $2,000 diamond wheel sharpener that'll leave a perfect polished point. If you aren't already pretty damned experienced, you'll probably never notice the difference between a piece of tungsten sharpened on a clamped down angle grinder and a 40 grit flap disc or even a plain old grinding disc and one sharpened to nearly a polished finish assuming your grind is consistent and your grind lines run parallel with the tungsten. Can I tell a difference? Yes, however for most tig welding the difference is small enough I'd rather just sharpen it with a grinder and cordless drill instead if I knew I had a few pieces of tungsten sharpened on a high dollar professional tungsten grinder if it would take me 5 extra minutes to get to.
If I was welding thin walled stainless, was testing if my razorblade welding skills were still up to snuff? Yeah I'm going to care waay more about how finely ground my tungsten is, but by then you probably already know when it does and doesn't matter according to your own experience.
My best advice for the best way to sharpen tungsten short of a 2k diamond wheel grinder? Get a bench top belt sander with a dedicated tungsten sharpening belt on it. I'd suggest somewhere around 120-240 grit for a decent combination between finish and rapid grinding speed, but if you can afford a few extra higher grit belts, experiment, figure out what you like for daily use and maybe keep a finer one for special jobs. Then just chuck it in a cordless drill, and with a glove on your finger, yeah, that part actually matters, that tungsten gets hot, grind your tungsten against the belt making sure to grind so that your marks run in line with tungsten piece itself at your desired angle using your index finger on your other hand to provide support on the tungsten so it doesn't flex on you. It's by far the easiest, fastest, most consistent and best finishing sharpening method short of a high dollar tungsten grinder out of any method I've used.
In my opinion those cheaper 300-400 handheld tungsten grinders are not even remotely worth it, the ones I've used have either left such an unbelievably coarse finish that made tungsten sharpened with a angle grinder hard rock look polished in comparison, ate up a good half inch of my tungsten within moments, and taken more effort to grind to a desired consistent angle than just freehanding it with a cordless drill and a flap disc. Not saying that goes for ever user's experience with every brand of those grinders. If they were cheaper or you could get one for free sure, but in my experience, I'd rather take that $400 pick up a desktop belt sander, more than enough belts and spend the rest on tungsten. Or even see if your local community college or welding school has a nice piranha 3 they might let you use after classes, then spend a couple hundred on an ahem, decent amount of tungsten instead, just be warned that if it happens to have a particularly well worn wheel in it, you're, uh going to be there for a little while if you have a handful of tungsten packs to sharpen. The head instructor at my school would probably take pity on anyone with a whole handful of tungsten boxes to sharpen if he knew it was getting close to time to swap the wheel anyway, but as they're $300 a piece, I wouldn't count on them offering. Before my school picked up a second one and put a fresh wheel in the first one I'd usually knock a rough point on a completely unsharpened or badly contaminated box of tungsten at home before finishing them on the tungsten grinder. Could be worth a phone call at the very least if you'd like a few boxes of perfectly finished tungsten for when you need it. I'm mostly joking about saying I'd rather buy $300 of tungsten and trying to find a professional grinder to use for a while before I'd get a handheld grinder, but well, not completely.
Generally when reasonable I like to keep a 10 piece box of tungsten sharpened on the Piranha for certain uses that I'll still occasionally show back up at school to bum 10 minutes on the Piranha to resharpen when needed.
I'd still suggest a benchtop sander with a moderately fine belt, silicon carbide might work best but ceramic belts work more than well enough. but if you're dead set on grinding your tungsten with diamond abrasives, I'd really try to find a piranhas 3 somewhere local they'll let you use. As long as I use a dedicated belt or flap disc/fiber resin disc that's never been used on anything else I've never seen any sign of any sort of possible contamination to the tungsten itself regardless of if I was using an aluminum oxide abrasive, ZA or ceramic, though flap discs generally don't survive long grinding tungsten even in the best situations and a cheap AO flapdisc will become useless extremely quick.
If you're lazy like me and use an angle grinder most the time anyway even if you have other options, those 3M 982c/987C fiber discs are absolute magic for tungsten just like they seem to be for anything else. I've yet to wear one out on tungsten before eventually I decide to do some heavy grinding work with it because it was close at hand and just dedicate a new disc for tungsten afterwards. I've never found a flap disc that lasts long enough on tungsten before dulling enough that I throw it away for it for me to have ever decided to do any other grinding with it.
I know nobody here even asked about any of this, but for any newbies who might not know this stuff I figured I'd post it. Also I didn't get any sleep last night so it may or may not be remotely coherent.