Glaive is helpful for this, too. You can't aim it up or down, and the lack of a crosshair makes throwing it a bit difficult, but because it's silent you can literally kill targets under the eyes of other targets without being detected, provided you're hidden properly.
Ash's Shurikens are silent and can be used while invisible. I made a build combining Energy Siphon, Smoke Bombs, Shurikens, Streamline, Fleeting Expertise, Continuity, and Constitution. The invisibility lasted long enough that I could waltz into one of the areas and just Shuriken everything to death, and they were so cheap that Energy Siphon provided more than enough energy.
Ash's Shuriken is silent, you just have to make sure that no other Grineer see the kill. Really though, you shouldn't even need it. Just have patience and the test is pretty easy. Don't rush it, just wait for the right time to strike.
Teslas are silent and therefore viable. However, if a Grineer sees another die, you lose, so be careful.
As a side note, Vauban's a pretty interesting option for stealth. His abilities are all silent, he can lock enemies in an unalerted state, and Bounce can help you get places where you won't be seen. He's currently my favorite non-traditional stealth frame.
I just beat this myself. The final platform that used to have two grineer on it only had one for me, making the final less aggravating. I used Loki with a little power duration and some energy siphon, and also brought along some team energy restore items due to impatience. Just went invisible, assasinated one or two grineer, then ran behind a corner when it was going to wear out (it has a visible timer over the skill icon when it's in use).
Just completed this test. Don't be intimidated by it, with patience and planning, you can get through it.
Room 1: Easy as heck, you don't need a walkthrough for this, just make sure the one NOT your target isn't looking directly at your target when you kill them.
Room 2: I found that killing the 2nd guy (the one that walks to the dead end) on the upper level first, then dispatching the other made this easier. Then I dropped down at the upper floor dead end and hid around the corner for that patroller to go past, and ticked him off the list. I failed once on this because my finger slipped and hit the attack button when I didn't mean to.
Room 3: Pretty difficult, but more than doable. First, I went to the left and followed that guy, but I instead took out the one directly ahead of him. I found that if you fall off the map, it puts you back at the beginning with no penalty, this is quite advantaegous. Then I went to the right and killed the patroller then, then the one directly ahead of him. The patroller down the middle is the one I took out next, as I fell off the edge and caught him as he was walking away from the start (the one on the platform also had his back turned).
This was my method, but I'm sure there are simpler, quicker and easier methods. Just remember that unlike some stealth games, Grineer can barely see a few feet infront of themselves. This isn't exactly about not being seen, but being able to dispatch enemies when the others aren't looking.