There is no way that would work with the IRS. Anything you estimated and can't provide documentation for will automatically be considered void and non-existent by the IRS if that thing reduces your tax bill.
If you think you have about $5k in valid deductions, but you can't provide any documentation upon an audit, then that $5k will be reduced to exactly $0 and you will owe all additional taxes plus interest and penalties.
What I always do if in doubt is to attach a letter setting out my assumptions. I've outright had to tell the tax authorities I didn't know the real numbers one year, because I realised shortly before filing that I'd lost documentation in a move, and so a whole bunch of details were estimates. Even that was accepted without additional documentation.
Of course I'm sure there are countries that are worse.