The question is complicated because you ARE allowed to eyeball the move, but eyeballing it is a form of measuring it. When does it stop being eyeball measuring and start being cheating measuring?
When you use something more than your eyeballs, it's not eyeballing.
If you look at a template lying by the side of the board you're not really using anything beyond your eyeballs.
Short of removing every object with a "known" size from the playing environment your standard seems more or less impossible to enforce. All a canny players needs to "cheat" (according to your definition) is foreknowledge of each template's reach when laid out on a grid of ship bases; the moving ship will always be present on its base, which would qualify as an illegal visual aid by your standards. Even if you could send the base into another dimension for the duration of dial-setting, there would be other useable markers -- asteroids, the 3x3 playing surface, etc.
WTF are you even talking about???
If you don't touch the template, you aren't using the template. Looking at something laying off to the side, then looking at the board, is not using a tool. If you pick up that something and try and line it up with something on the board, it is using the tool.
If you can judge something purely by the knowledge contained in the game state, power to you - someone pointed out recently (which I hadn't caught, personally) that if you're shy an asteroid you can (minus the nubs) guarantee a safe 4 K-turn, because the asteroid is at least 5 away from the edge. That's using game knowledge, not tools, and is perfectly fine.
Seriously, this is starting to get silly. You cannot use tools. Your brain, in this case, does not qualify as a tool even if you normally follow the "don't use it" standard.