Hi,
Without an access to the front end, it would be difficult.
Please add a new element in the #__hikashop_config table.
config_namekey : bootstrap_forcechosen
config_value : 0
config_default : 1
It would remove the Joomla 3 chosen initialization.
But as I already said 2 times, this is not an HikaShop bug. This is a Joomla 3 Template problem.
Regards,
Jerome - Obsidev.com
HikaMarket & HikaSerial developer / HikaShop core dev team.
Also helping the HikaShop support team when having some time or couldn't sleep.
By the way, do not send me private message, use the "contact us" form instead.