I bought one of the Hodge Silk Oboe Swabs suggested by Clint, from Amazon USA. So far that has worked fine for me but your suggestion of the piccolo swab from BG is useful too.
BTW MacOS Big Sur didn't need a driver for the Behringer Line 2 USB but Windows 10 users will need to install the ASIO4ALL driver software (linked from the Behringer product page too).