This is how I was able to get borderless printing on an envelope using Photoshop and a Canon Pixma inkjet printer without smudging. You may be able to use other graphic design software, such as Illustrator etc, as well, and I believe many other Canon printers have the settings necessary for the task. If you have a different kind of printer, look at the settings I've got here and see if your printer offers settings like it.
Note: I can't confirm if this will work with ALL the edges borderless, as I only needed one. But if you get the placement right in step 6 I imagine it would work.
Step 1: Go to Print in Photoshop, Then Print Settings
Create your design in photoshop on the exact canvas size as your envelope in landscape, so you can see visually how you want it to look printed out and to be sure it will actually print that size.
If printing on the back as well (as I was), Make sure there isn't any artwork along where the edges of the envelope flap will be. I can't confirm if it will smudge or not, so better safe than sorry if you can help it. When I did this, I just stuck an envelope to my screen and zoomed to the exact proportions in photoshop (I actually had to input the actual numbers, in the very bottom left corner you can see and edit the zoom proportions...mine was 44.3%) From here I used the rectangular marquee tool and traced along the bottom of the envelope flap then brought the mouse to the top of the canvas and let go of the mouse button. This left me with a rectangle that represented the top of the envelope to the bottom of the flap. I made a new layer via copy out of it, brought it to front, and then filled it with a color, and would tun it on and off as I moved the elements of my envelope to make sure nothing was too close to or crossing the threshold. Be mindful, though, of the left and right diagonal edges as well, if your envelope flap is die cut and doesn't go all the way to the edge. You can tweak if necessary during test prints. You may even be able to find templates that show this edge online, I don't know. Sorry for no pics and if it's not descriptive enough, but I wasn't planning on writing a photoshop tutorial =)
On to the printing:
When you first go to print in photoshop, select Print settings on the right-hand side.