I've been doing some at-home preschool with my 3 year old over the summer. She loves to cut out, but I've found that pictures that don't have dotted lines are a little tricky for her to just cut around the outside. See poor baby Moses basket was in three pieces before we glued it on the water. Not a big deal, but I didn't want to have to recapitate baby Moses, so I came up with a technique to make "where to cut" a little less fuzzy.
We'll use Phil as an example because he was on a piece of scratch paper I had. He appears a little concerned though doesn't he?
I could see Phil a little better than you can in this picture, but I did find that it was easier to see through the paper if I put it on a light colored surface as opposed to a dark one like wood.
I traced around the picture where I wanted it cut out with a marker. While your tracing, you can smooth over any sharp corners that you think might be a problem.
Voile! Had it to your preschooler, and tell them to cut on the "purple" line on the back of the paper. That's what we did with baby Moses, and a you can see, my preschooler is pretty good at cutting.