Paying in cash still counts.
Just because you paid someone in cash doesn't mean it doesn't count, or that you don't have to account for it. It can't just disappear off your books. If it's a local handyman that asked to be paid in cash, get a receipt, or give him one and have him sign it for you. Your bookkeeper will enter it under Repairs & Maintenance and it will reduce your income, and your taxes.
If it's a regular thing and you pay someone over $600 for their work in a given year, you are supposed to provide them with a 1099 January of the next year.
Or, you can code it as Owner's Draw (money you took out of the business for personal use) and it won't decrease your income, and you'll pay the expense without the benefit of it decreasing your income and taxes.**
One way or another it will be recorded on your books. Being a bookkeeper and caring about your business and your time, the quality of your experience, I always want to see you correctly and completely, descriptively and accurately enter every transaction. That kind of consistency makes it easier for me to do your books, and leaves me with fewer questions for you.
As a bonus, correctly and completely recording cash payments as the expenses that they are will make it easier for your accountant doing your taxes — maybe s/he'll charge you less than last time if your books are easy to read and understand. And, every item correctly and completely recorded on your books not only makes your books a useful tool to analyze, understand and improve your business, it also does not increase the likelihood of an audit or fines.
I don't know what increases the likelihood of an audit, but I do know that doing it right the first time doesn't.
The cash was real when you earned it; it was real when you spent it. No less real than if you earned it or spent it via check, credit card, or ACH transaction. It needs to be recorded on your books and on the books of the person spending it or receiving it. Really.
It's not just the right way to do it, it'll be easier that way.