I would boil the water. Not because of contamination but because of oxidation. If the yeast are anaerobic, then I wouldn't want to introduce oxygenated water. Boiling will remove the oxygen. Then, you can either add the honey at flame out, or any temp. below that, all the way to 105-110.
Way I see it there are a few things going on there...
1. We're talking about 4-8 OUNCES of water to start with here.
2. You'll introduce oxygen/air as soon as you pour the solution into the fermenter. That is, unless you're using a bucket, and plan to pour it in an inch above the wort you'll still get some addition.
3. I am curious as to how long you have to boil water to remove excess oxygen from it.
I don't use tap water for anything going into my brew. I use filtered water, so maybe that's either removing, or stopping extra oxygen/air from getting in. Anything I'm either going to drink, or eat, that is made up of, or uses, water gets the filtered water. The filter system I have sits under the sink, and comes out via a spout/tap in the actual sink (opposite the sprayer hose). I do know that there's no aeration going on there, other than what happens when the water hits the vessel, or other water (so minimal at most)...
I suppose that if you're using tap water, with an aerator attached, you would want to remove the extra aeration from the water. So, boil the water the day before, then seal it up and set it aside for use later...