I'd bet the tulip poplar whips will be a breeze. Liriodendron tulipifera are generally very easy to transplant, and now is a good time to do it. Below is a link to my guide for planting trees and shrubs. I hope it will be of some use.

The sassafras may be a different story. They are notoriously hard to transplant. My suggestion is to wait until after leaf drop and keep as much of the rootball intact as you possibly can. One reason you don't commonly see Sassafras albidum in nurseries is because even pot grown specimens (which you'd expect to be tremendously easier to transplant) often don't survive planting out. It can be done, but it's just going to require a little more work and attention to detail.

BTW, if you have a mature sassafras within a short distance of your flower bed, the small saplings may actually be root suckers. Root suckers are more common than seedlings and can be even harder to get to survive (because of the limited amount of roots usually available).

Here is a link that might be useful: Planting a Tree or Shrub