For a double bevel knife, do as follows:
On each side of the knife, pick an angle (about 15-20 degrees is good), and re-establish the bevel until you've gone all the way down to the edge at that angle with however many strokes are necessary. The angle doesn't have to be perfect - just make sure you don't start getting steeper than their angle you initially started at.
After that's done on both sides, keep roughly the same angle and work on both sides of the knife, flipping it with every stroke. This will work the burr off and leave you with a clean, sharp edge.
To get your blades really sharp, and help remove the burr, you can also use a stropping compound, such as Chromium Oxide (the green stuff) on leather or MDF, and strop away from the cutting edge, alternating as you did before, and keeping a low angle. Flip the knife over the spine, not the edge, to ensure that you don't accidentally roll it. You can go quite far with the strop if you're careful not to round over the edge - just remember that leather will give and flex.
In the sharpening process, don't worry about working the edge and staying there. Make sure to work the entire bevel, and take the back down until you've reached the edge in the initial reforming of the bevel. You'll know you're down to the edge by feeling the opposite side for a small burr. Then you can work the other side, and continue the process as I described.
Sharpening free hand isn't that hard - just takes a bit of practice. I wouldn't worry about ruining a double-bevel knife. With a little time in, you'll get quite efficient at this method and it won't take you long at all. You'll never use a dull tool again when you experience one that is properly sharp
I do not recommend the V-type sharpener things that you mentioned.