I don't think you can share the FamilyEcho link with someone without displayed life dates. Depending on the size of your family tree, it might be an option to make another tree without birth dates?
Another idea I'd have is to change the family tree view to "Complete", disable life dates in your options, and then turn the tree into a PDF (if you click on the "Print" option, you can choose to this). You could share the PDF with who you want to share without the possibility of them toggling birth dates back on, but depending on the tree size it might be a bit difficult to view.