Looking at Brian's picture in post #9, as near as I can tell, they look like 6mm slots about 6mm apart. If so, a 6mm router bit has two cutting edges rather than 3mm bit I mentioned above, (which only has one and has a narrow shank), so the 6mm bit will be more robust and will make more progress, with the two cutters.
As to using a router bit in a pillar drill, I've never tried it, but the limitations need to be understood. A typical hobbyists budget-priced 5-speed pillar drill such as the Screwfix one at the link below, will have a speed range from about 500 to 2,500 RPM. Thus, at the maximum speed, using a 6mm router bit, with each rev, 18mm of wood will pass the cutting edges of the bit. So 2,500 Revs x 18mm = 45 Metres of contact with timber by the router bit cutting edges per minute.
https://www.screwfix.com/p/energer-e...E&gclsrc=aw.ds
The same 6mm bit used in a router running at 30,000 RPM x 18mm = 540 Metres of contact by the cutting edges with the timber per minute. (Yes, half a km per minute). If the router is advanced along the timber at a rate that the bit and the timber are happy with, it will cut very cleanly, even across the grain, with no tear out.
A hobby drill press will typically use a belt-drive 350 Watt motor. Most budget routers, such as the palm router I mentioned in my earlier post, will be 700 Watts upwards, so not only do they run at a speed 12 times fast than a pillar drill, the motor is more powerful. That's why they can be so scary, made all the scarier because they're hand held - both hands, unless used in a router table.
Eye protection and a dust mask are essential. Best not to use our lungs as 'air filters'! Personally, I've always worn ear defenders whenever I use power tools - hammer drills, routers, circular saws, bandsaws, lawnmowers, hedgetrimmers. Still got good hearing, unlike many of my chums of a similar age who need hearing aids.
Hope that might be useful.