Putting time stamp into cell with single click

I have a spreadsheet to track times of certain milestones during a project and want to see if it is possible to have a macro that simply puts a time stamp into a cell when I click on it under the appropriate column and the appropriate row. See attached spreadsheet example. The cells involved are orangte colored that I am working with. Thanks in advance for any suggestions and help.

Sub TimeStamp()
ActiveCell = Time
End Sub

Now based on this macro using a button, could it be possible to have the macro read the Start Time column and compensate for the time difference? In other words, when I click the button with the selected cell, it will give me the current time, which is CST. Is it possible that when I select the cell and then click the TimeStamp button, it will see what the Time Zone is in that particular row and show the time as it would, say for EST, an hour later, like instead of 10:45PM for CST it will show 11:45PM. Or if the row is showing that is is MST, it will show 9:45PM instead of 10:45PM when I click the TimeStamp button. Can this be done? Thanks.