What you do on your time off should be of no concern to an employer. Request the time off, get it approved and go do what you have planned: hunt, play tiddley winks, sleep...whatever.
Pretty much all the places I've worked it was pretty cut and dry - So many people were allowed to schedule off on any given day, if the day was open and you requested it, you got it.
I've also found that if you treat the employer like you would want to be treated if you were the owner/boss, they are more willing to work with you when things come up.
Calling in sick is one of my pet peeves, sick days are for being sick. I've never called in a bogus sick day my entire life, since I was a teenager with my first job until now 35 years later. If I called in sick, I had my head in the toilet or something serious going on, and I can count those days on my two hands. A lot of the bogus stuff is what sours employers on being understanding.