First, I think the OP is smart for wanting to pay taxes on his income, whether or not the IRS has a record of said income.
Second there are lots of reasons for paying taxes on your income, even if you obtain it through shady or illegal means. What did they eventually convict Al Capone of? Tax evasion. It didn't matter to that he was a gangster --- if he had only given the government its cut, they wouldn't have been able to nail anything on him.
I know of drug dealers and illegal immigrants who pay income taxes. Some illegal immigrants even pay Social Security taxes.
Talk to a couple of tax accountants and figure out how to deal with this. The IRS can and will mess you up worse than the justice system, so it's best to CYA when you're dealing with them.