I would do this with a modified MFK700, but the bit would be the same in your case. The one I use is a 3/4" diameter, 1" cut length and 8mm shank. It is a simple straight bit.
Poplar is pretty forgiving as long as you avoid knots, and don't take off too much material at a time. If you have your edging within 1/16" or so, you should be fine.
A spiral or even sheer bit would be better, but will cost significantly more too. If it was Maple, especially if it was curly at all, the spiral would be a better choice.
Most of the sheer cut bits will be flush cut, with a bearing. Of course there is nothing preventing you from taking the bearing off. I have done that before, but it was only a 1/2" diameter.