One thing you could do would be to do a ydna test on Charles. With a male you have a direct line link to a surname. If he is adopted he should match with a Fox surname or another. If he is a Wilde then most likely he should match with other Wilde's. There is a small chance that you might match with others and maybe find a connection. It's not cheap but it may be the closest you can get to the adoption answer. Now you may match with other surnames as well so don't let that worry you but it's another option. Your best bet would be to order a 67 marker test. It may take about 6 wks to get all the results back. You usually get the 12 marker in 2 wk, the 37 marker in 3-4 wks and so on. Let me know if you have any questions.
Here's the link to the dna company that I have used:

http://www.familytreedna.com/Default.aspx