IMHO 640nm is going to be a better choice than 650nm or more likely 660nm. You will get more bang for your mW. If you are replacing a 200mW 650/660 with a 150mW 640, you'll get a better saturation in your reds, oranges and yellows. It'll just cost a little more.
Depending on the module, you should be able to press-fit the diode into the aperture by tightening the unit in a vice. The key thing to do is make sure you use a cylinder-shaped "tool" (could be the hollow part of an old key shaft) that surrounds the diode can, but presses equally on the diode base to push the diode into the aperture. So by lining up the left side of the vice, then the cylinder tool, then the diode, then the module, then the right side of the vice, you should then be able to tighten the vice and get the diode press-fitted nice and squarely into the module.
Get the new diode, use anti-static precautions. Blob some solder across the cathode and anode. Then get the LASORB, carefully bend the bins towards each other, then bend them parallel to each other so that the result is that the LASORB pins are about the same distance apart as the cathode and anode pins. Give each pin on the LASORB a pinch with a side cutter, so that it creates a little recess the diode pins can rest in. You should then be able to connect the LASORB to the diode (ensuring the appropriate pins of the LASORB connect to the appropriate pins of the diode) with no solder and the two should "clip" together. if you hang the LASORB off the diode pins in a vice or similar, you should then be able to solder the LASORB more permanently to the diode. Also solder the driver leads to the diode pins. The recess (clipping-on) of the LASORBs you created will help keep the LASORB in place even if the solder melts whilst attaching the wires During this process you may have inadvertently separated the solder blob. Well... if you have the LASORB in place, then this is exactly the outcome you want, otherwise once the wires and LASORB are in place, quickly soften the solder blob to separate.
You should be good to connect to the driver by then. Just be sure to check your 0v and 5v modulation signal positions with a meter across the diode connections before you do connect to ensure that the min and max current (in mA) is set according to the diode you choose.
Then post here and tell us how you got on, with pictures and a how-to guide for the rest of us