I'm using an HP Compaq 2710p with the Wi-Fi card replaced with a Broadcom
BCM4311. (That's one of the cards the 2710p laptops come with though if I'm
not mistaken, no idea if the BIOS would entertain the idea of a Wi-Fi card
that's not the default in any of the 2710p's).
A Compaq TC1000 might also be a bearable option (after the wi-fi card's
replaced with one that supports WPA2 anyway), apart from the slowness I
experienced with LXDE on it (LXDE, that was not a typo!). Maybe the TC1100
would be better (they didn't lock laptops to Wi-Fi cards back then so just
get a random Wi-fi card that works with non-proprietary drivers and fits the
slot).
I guess shopping around for old, used x86 convertible tablets can't hurt. The
lack of proper touchscreen on those laptops may be a different question,
though.