Yes, deleting an invoice will affect your Accounts Receivable and Balance Sheet. Instead, you'll want to void it then create a Journal Entry to offset the amount. This way, QuickBooks will keep the invoice number and list it in reports but changes the amounts to zero.
Before doing so, I suggest consulting your accountant to guide you with the correct debit and credit accounts to use.
Here's how to create a journal entry:
Go to the Accountant menu.
Choose Make General Journal Entries.
Fill in the necessary information by adding the account from which you are moving the money.