Yes, it is possible to remove the ability for a user on the Shop Floor Insight web client to select an activity from the “Activities” button.
This is done on the Shop Floor Activities page in BC/NAV. Find the activity in question and uncheck the “Generate Barcode” value so it is OFF. This will remove the activity from the drop-down list in the SF web client. It will also prevent the activity from appearing in the list of barcodes when you run the “Generate barcode sheets” report.
However, this will not prevent any user in BC/NAV from selecting the activity onto their timecard manually if they have BC/NAV access.