An option may be missed here. Depends on the age of the house but if it has some type of quarter round or base shoe to trim out the wall, it can be reasonably easy to hide a hole if you pull the trim away from the baseboard, drill carefully in that space and then you can run a larger tube, depending on how much the shoe will cover later.
So the question can become why and when you need to cover the hole. If in rental, this is a preferred way as there is no damage showing when the trim shoe is put back in place.
If you are an owner and just needing to avoid holes in really good flooring, another thought might help. A long bit, drilled at an angle, can go down through the sheet rock above the base trim and on down through the double layer of 2X inside the wall and come out in the basement below.
I might suggest using more like a 1/2 inch ID tube to get the job done a bit quicker. One can reduce the size of the outlet down to fit 1/4 inch but that leaves a pretty long term project if you change much water.