I don't recomend using a clamp cause the rotation could damage the diode or press it diagonally. Better use a vice, in the end you will end buying one cause is a must have tool. It costs less than a diode and you can use it for a lot of things.
In my experience I have used a C-clamp successfully but it's VERY difficult to center the diode level in the module. The beam will come out crooked. If you roll the completed laser on a table while it's on you see that the beam traces circles on the wall.
If you have, or have access to, a drill press...
Get a 1/4 in aluminum rod cut to about 4 in in lenght. Drill a hole in one end of the rod such that the leads of the diode will fit into the hole. Now install the rod into the drill press, hole side down, as you would a drill bit. Now use the press to install the diode.
That was my idea too - a vise is so cheap that ruining even a single diode using a c-clamp would likely cost more that buying a vise in the first place.
Also, its just a good tool to have, and it will prove handy in more situations that press fitting laser diodes. Using a vise to clamp down things you want to use a dremel on and such will prove very convenient.
I use my vise regularly, and its not even mounted on a working table. They just apply perpendicular forces where you need them, and a lot of force with little effort compared to anything else. Since the costs are so tiny, its a good tool to purchase, even if you could fiddle your wau around using one for some applications.
I recently got one for ~$10 from the same seller. The quality is reflected in the price, but to me that was all the quality I needed! I have successfully extracted and soldered 3 laser diodes in the past week, using one clip and looking through the glass. The clips are STRONG and can hurt a little, deff enough to hold little parts.