If you do rent a machine, take it out back and practice until you are comfortable. I have dug close to the house without a problem, but it takes 100% concentration, 100% of the time. My mind drifted for a second and I almost took out a column on my front porch. Luckily the machine controls were responsive.
The arm of the mini-ex is slightly off-center, so work with that side closer to the building. you will want to work from the far end and back up the machine as you go.
And I would consider doing the final layer of dirt - that is stuck to the wall - by hand after the trench is dug.