You can check the WI DNR Find A Lake page for Burnett lakes with smallies, most look to be in the Webster area:
https://dnr.wi.gov/lakes/lakepages/Results.aspx?location=7&page=SMBASS&letter=ANY
My family has cabins near Little Wood Lake, and I have never really heard of a smallmouth bite nearby. The only water on the DNR list of smallies I have fished is Yellow/Little Yellow/Yellow River, but there I’m primarily targeting muskies. Haven’t caught an incidental smallmouth there yet.
If you really are seeking smallmouth water, I’d probably start exploring the Croix. You’re just going to have to take it slow and will be limited by water levels unless you are in a kayak or canoe.