You need to get onx maps - on your phone. There is a free 7 day trial, and 29.99 annual fee (for one state of your choice), and worth the money.
This lake area you are interested in shows as being surrounded on 3 sides by the park google maps - each boundary within a half mile, and onx shows it being surrounded by private timber companies by hundreds of feet on 3 sides, still a half mile or so out of the park.
Provided you have a phone with some memory left to spare - it is a no brainer and it will not only save you big $$ in trespass fees, your downed animal, etc, but will also show you new spots legal to hunt.
And no, this is not a commercial endorsement for onx - just a user satisfied.
The best of luck