Here’s a possibility:
Add the cash accounts and update normally. All transactions will download.
Set up AutoCat to categorize any transactions in these cash accounts as a Transfer. In this case, the AutoCat rule has a blank Description field, but names the cash account in the Account Contains field. Your cash transactions will now be excluded from budgets and reports. (caveat: I assume that AutoCat Rules accept a blank Description field, but I haven’t tested it.)
Turn on Filters for row 1 of your Transactions sheet. Use the Account column filter to exclude the cash accounts from the filtered view. Use this filtered view as your normal view.
Once set up, your cash transactions will be hidden and unreported, and balances will be current without any further actions.