It just becomes natural with practice. Don't worry about it,
and ride both unicycles a lot.
Your mention of psyching yourself for your giraffe reminded me
of something. Almost a year ago, when I bought a giraffe after not
riding one regularly for 15 or 20 years, I discovered that I couldn't
free mount it. This was quite discouraging, even intimidating. I
tried, and I fell; I tried and I fell; etc. Eventually, I started
getting up a reasonable percent of the time, but I still chicken out
and curb mount whenever I know anyone (particularly, my wife) is
watching. I need to follow my own advice, and ride it more often.
Craig Milo Rogers