It can affect your credit momentarily until you’re able to bring down your debt. In the long term, closing a card in good standing with a 0 balance will not affect your credit.
Closing some cards would bring down your available credit, and keeping the same debt will raise your debt to credit ratio, and this can momentarily bring your scores down, but once you pay this debt your scores should come back up.
If you do not want to see this short term change in your scores, the best thing would be to pay off the debt first and then close the cards but if this is not possible, then you can just do the balance transfer and keep paying…