It's not good to mix, but if you're going in a straight line most of the time, and you're not prone to doing exit ramps at double the speed limit, there won't be a problem.
Before drag radials came along (back in 70's and 80's), almost all vintage Musclecars were shod with modern radials. It was common to bolt slicks on and go street racing for the night, or perhaps hit the dragstrip. It was rare that all 4 tires were changed over to bias, usually just the rears.
The reason you're not supposed to mix bias and radials is because the sidewalls flex at a much different rate between the two. If you have to do a emergency maneuver, the front (radials) will dig while the back (bias) will slide. So yes, it could be dangerous. But the tire manufacturers always make it sound like if you mix bias and radials, your car will explode.
Personally, I would change all 4 in order to get predictable handling, but you can run bias/radials at the track without any problem.