How to easily dismiss single cell from a SUM formula?

Hello from Bilbao! My first post:

My spreadsheet is being used for payroll and is shared with a colleague. It's a simple enough sheet in some ways: a list of employees names, the number of hours overtime they've done each month and then a total column.

However, at certain points in the year my colleague will extract these hours and forward them to the finance dept. Ideally, I'd like those figures to always remain visible but be removed from the final total column (which will be called something like 'Total hrs still needing to be paid').

Obviously, she could change the SUM formula but my hope is that either by shading or with a click of a tick-box (check-box?) she could more easily signal to individual cells that they no longer count.

Any suggestions?

Many thanks.