I am in line with what they say here.. The compression bits are the not up, and not down, but kinda both bits, because unless you are on a CNC a lot of the spirals are a bit wiley, and can get squirrely quicker than a flush cutter with smooth sides. You've already had squirrely, you want tamer.
For your use, tracing an edge on a piece I like a piloted straight flush cutter, but I like the really much bigger diameter than you might think you need, school of thought. I haven't gotten any of these yet, but they are talking my language. I do have a few that are 2 blade 1 1/2" diameter that I routinely use to template rout with, provided there are no straight pieces where the bit would trap. For this Infinity bit it has a hybrid edge, it's a sort of a compression bit, packed as a flush cutter with straight sides.
https://www.youtube.com/watch?time_continue=2&v=Hr29KWj1ELc
I like the short widebody for a router table, running against a pin, and hopefully Santa is bringing me one.. Costy, yes, but they are designed for what you are doing, which is also a routed edge, that isn't standard fare for most router bits out there, the slow curve. That board design is the rage, and yes I too, have no understanding how a person can bandsaw that curve, and NOT flush it up, never have I heard of a glue line ready BS blade.
But no matter what bit I am using, NO FENCE. I do them off a pin on the router table, or handheld. Handheld direction is a challenge, if you suddenly find yourself making a climb cut freehand, and DON'T know it's coming, that workpiece will go zippity do dah, faster than a lot of us can recover, and you will scream past a piece of the bit you don't want to. Handheld you can also do them off a template, still be aware of climb cuts.
So 2 of my rules of routing. Pins can look scary, but they are really the best way to control the work, and not have the work, just bang into the spinning bit. If the piece is BIG, you can hold the end not at the cutter, and you will be removed from the bit by your workpiece. Being in control on the opposing side, you not only have a distance, but you gain leverage, and leverage is control over the pin.
If it's a short piece, do NOT hold onto it, if the piece does do that zippity thing, your hands are right there. Instead use some type of work holder. Climb cuts happen in hand held, or router table use whenever you go against the grain. On your curvy edge you likely went against the grain a few times, but were thinking straight line, well sorta.
You can buy something like this.
You can make something like this. Note the nice cover over the bit, you can make a safety bar to mount anything you want to a router table, not just a fence. Just make sure it's secure.
Best bet yet is you may already have a great work holding clamp laying around. Hardly anyone uses them for clamps anymore. Mine were from a time before dirt.
Always do a practice run through, with power off, look at what you are about to do, wonder what could go wrong???? It won't be long before you'll wonder how you ever made a mistake. Wood mistakes, while a PIA, are actually just a little extra time. Other mistakes can be serious injury, so always use that best tool, yer brain.
Best safety practice, is if you look at something, and it just sux, every way you look at it, you see pain, and trouble. Ask a question here.