A lot depends on the condition of the wood you are attaching to.

Can you make the screws come up tight in the old holes?

If the wood is still solid enough for the screws to be tight you may not need to do anything.

If any are NOT tight you can try a couple thing.

If the wood is thick enough adding 1/4 inch, 1/2 inch, or even 3/4 inch to the screw length will get you into more wood.

Even going up one screw size (larger diameter) may be adequate.

You may need to adjust the countersink in the hardware for larger screw heads.

Or, you can glue(Wood glue) a toothpick or two in the old holes and use the original/replacement sized screws.

"Or, you can glue(Wood glue) a toothpick or two in the old holes and use the original/replacement sized screws."

If the shutters can fall on anyone I would want a little more of a sure bite into the wood.

I use the "toothpick" and glue trick all the time. Instead of toothpicks, I prefer hardwood dowels. Usually a 1/8" dowel works great. Leave the glue to dry overnight before drilling the new pilot hole.

Even a broken-off brass screw can be drilled out and restored using a 3/8" dowel.

Thank you, thank you..! Although the wood seems stable.. to best of my knowledge (the screws were a little loose previously, but there was some rust, too) they're only over 70 years old.

I have toothpicks, and will pick up some 1/8 dowel tomorrow... should I expect my drill to just power through either?

Thanks again --

D.

"should I expect my drill to just power through?"

Still drill a new pilot hole. Pick up a Vix bit, a self-centering drill bit.

The reason for letting the glue dry overnight is to get a good pilot hole, without removing the plug.

Here is a link that might be useful: Vix Bit