Louis f sockalexis autographed ball

[jmcd]

I have a ball that is signed by Louis F Sockalexis. It was given to me 42 years ago by an old neighbor. He knew that I collected baseball cards and memorabilia and he had it in a box in his garage. He said that his father gave it to him. I know that his family lived in the Chicago area but I don't know much more than that.
I had one person who authenticates autographs look at the ball and he told me that the ball is from the correct era and that he believes that it is authentic, but he said that it would be very difficult to actually authenticate the signature. The ball was coated with shellacque at some point after being autographed.
I'm just asking for opinions or any information on the steps to take to possibly authenticate this. If it's real, it should be in a museum, and not locked away. Thank you!!