Microsoft's own guidance on password protection of worksheets in Excel 2013 includes:
Remember, though, that this type of protection doesn't encrypt your files. Users can still use third-party tools to read your data.
Also to note that password protection in Excel 2013 is different to earlier versions of Excel, if you save a workbook in the earlier non-XML format (i.e. .xls) it will remove the password.
The evidence suggests that Google Spreadsheet (like the earlier versions of Excel) does not support the Excel 2013 standard for password protection, so the answer to your question looks unfortunately like it can't (currently) be done.
I do not know Google Spreadsheet, but to achieve what you want, it does look like you will need to use whatever controls are available in that application.
And for avoidance of doubt relying on such a control for something critical would be unwise, but given the scenario you are trying to achieve it does seem like a sensible level of protection to apply.