I usually use a spouted measuring cup or the blender jar (the Blendtec small Twister jar is perfect as it has an elongated spout that almost perfectly matches the width of the molds) unless the mixture is quite viscous, in which case I scoop it into a zip-top freezer bag and cut off a corner to use it like a piping bag, as @Tri2Cook suggested.
I have the same 10-pop mold that you do, @MelissaH. I found it sometimes difficult to remove the lid, especially if I accidentally nudged the sticks in a way that they were no longer parallel and frozen in slightly different directions. So I skip the lid and freeze until the mixture is slushy enough to support the sticks (usually 30 - 45 min or so) before sticking them in. This method does run the risk of having the mixture frozen solid with no sticks if you forget. So far, that hasn't happened to me, although there was a very close call with last night's peanut butter and banana pops 
- timers are good!
I keep a small cookie sheet in the freezer because it helps keep the mold level on the wire shelf and then it's pre-chilled and ready to place the unmolded pops on. When I remove the mold from the freezer, the cookie sheet comes along and gets a fresh sheet of waxed paper on top.
I have a rectangular plastic container about the size of the mold that I fill with tepid tap water so that the filled mold parts can be immersed until I can pull a pop out. Usually 10-20 sec, though it varies a lot. Boozy pops thaw quick. I used to run hot water over the molds but I was afraid I was using too much water so I switched to this method, then I can take the water outside and water plants.
As soon as I can get a pop to move, I put the mold on the counter next to the chilled, waxed paper topped cookie sheet, quickly remove all the pops and put them on the waxed paper and put them back into the freezer.
After they've firmed back up, I transfer the individual pops to snack-sized zip-top bags and toss them into a bigger freezer bag.
I used to do sort of the same thing you did, folding the waxed paper over the pops and then folding the pops up accordion-style and placing the package in a larger bag. I hate the waste of the individual bags but it's easier for giving them away or serving to a group and results in less freezer-burn. When I eat one at home, I rinse out the bags, dry and reuse them.
I usually give the sticks a quick rinse before I use them and check for loose splinters but I haven't done any soaking comparisons.