Depending, it's possible you can 'drill out' the plastic. MAKE SURE you use a BRAND, NEW drill bit. It may need to be a little bigger than the hole, itself.
BEFORE you get all excited, buy the drill bit and pick a 'hole' that's closest to the floor. Take a light-weight hammer and a nail, and make a nail-mark in the CENTER of the plastic putty. Then, set the center of the drill bit on the putty, and drill. DON'T press too hard because under there is a nail!
While you're at the store, buy the putty that's just a SHADE LIGHTER than your stain's color. (IF you can, bring a sample piece of stained, oak wood w/you from home to the store for matching purposes. Take it home and stir up a can of your stain. (Remember - Stir your stain CONSTANTLY because it has 'solids' in it that need to remain 'suspended' in the can. THAT'S where you get your pigment/color from.) Dip your thumb and Index Finger in the stain and roll a small amount of it THROUGHOUT a piece of putty. Hopefully, it darkens just a little. If you'd like to experiment w/how light or dark you should go, take your sample piece of wood and predrill some holes in it. Just be sure to label your holes so you know which is which (when it comes to 'how much' stain you had on your fingers. (Maybe you can write on the back of the wood, or put a piece of masking tape across it to write on.)
After that, you should have your answer. Usually, a Finish Contractor does what I described when it comes to matching the putty to the stain. Since you're gonna have to drill out your holes a little BIGGER than they were done initially, you may notice it a little. It will be your call as to whether or not you like the job. Remember to tap a nail in the center of the existing plastic putty. This will help prevent the drill from 'sliding' when it's turned on. Oh, you COULD try to pre-drill the plastic putty out w/the same sized drill bit that was used to predrill the wood. (If your husband didn't pre-drill, get a drill bit that's the width of the finished nail/screw head that he used.)
Others may come along w/advice so HOLD OFF and stick around a few days. My best to ya and hope this helps.
Jay J -Moderator
PS: The Home Center stores out there have various shades of putty ...