Question 3-way switch , no meter or continutiy tester?

Good luck, the beeper is an inductive type tester and it will sense a voltage within a couple of inches. This means it will tell you that all of the wires are hot. Where the power wire is feeding the system can be different in any of 3 types of installation. If the feed goes to the light is one case, or it goes to 1 switch and the light wire is in the same box or the power goes to one box and the light is in the other box. Get an analog meter, or a relay type tester and learn to use them. Contact a qualified professional electrician to do the work, it's safer and faster.

There should be a 2 conductor and a 3 conductor cable in the switch box. The wires connected to the switch from the 3 wire cable are travelers if this is not the case, describe what you are trying to do and the wires in each box, then maybe we can help.

The common wire should be attached to the discolored screw on the switch. Also, typically if the two white wires in the box are tied together you'll have 3 wires remaining. A black and a red should come from one cable and just a black from the other cable. The black by itself is the common.

Or if there are just three wires total in one box, the white should be used as the common and taped up or colored with a marker.

But like I said, the discolored screw is the common

Your method ought to work, if you use a heavy enough wire and are very careful AND the light is connected to the other switch. Sometimes the power and the fixture are routed through the same switch box, or the power or common wires are routed through the fixture box; but in these cases there will be more wires to one of the switch boxes than the other.

But really, continuity testers are cheap.