How can I report cash income while on EI?

I have never been on EI before and I am about to be layed off from my fulltime job due to downsizing. I will qualify for EI, but my question relates to a part time job that I have on weekends. I am self employed at my part time job and get paid strictly in cash (so there is no record as to how much I am making, or that I am making any money whatsoever. None of the cash goes in the bank, and there is no record of me being employed or self employed). When I do get layed off, I would like to be honest and report my self employed cash income to EI. My buddy says that if I report it, EI will hassle me and accuse me of making more money but only reporting some of it, so that they would be able to cut me off from receiving benefits.

I don't make enough money off my part time job to live on, but I also don't want to be penalized for being honest and reporting what I make. Is there a way to report this income without being hassled for my honesty, or would it be better to keep my mouth shut, as there is no record of me making any income or having any part time job?

I don't know if this matters, but I am in Ontario