Depending on your customer base, One very simple bit of code:
pointer-events:none;
See browser support here: http://caniuse.com/pointer-events
Edit: just in bed and maybe think about a different solution, but can't check on my phone, but maybe the jQuery mousedown trigger might be an option to hide the arrow for a split second for a moment before the click, maybe?
Or this, not sure how it will be used, but saw it in another thread: $ ('# Select-identifier') show () focus () press (); ...
If I were on my computer, I would test it ...
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