Disclaimer... I'm currently on my surgery rotation.
The issue is that if you want it to be truely sterile, you're going to need a mask, hair cover, and sterile gloves, at a minimum. Otherwise it isn't sterile in the strictest sense, and definitely anything touched with exam gloves is no longer sterile. Sterile and clean are two completely different things. There's a reason why the suction catheters in care facilities are encased in plastic for easy and repeated use.
/Yes, sometimes I get too pedantic
Clean hand and dirty hand