I canoe at 3 mph without a helmet. I flat-water kayak at 4 mph without a helmet. I motorboat at 30 mph without a helmet. I drive (at 100 mph in Germany a few weeks ago) without a helmet.
I wouldn't white-water kayak without a helmet, because if one rolls, there are rocks down there. Even if not completely inverted, but sideways, smacking a rock is a possibility.
So, yeah, it raises the question for me: is this more trip than you think it is? Or are they being overly conservative on this point or perhaps have a blanket club policy or insurance rule?
Back on topic - does the club require any particular specification (like UIAA certification for climbing helmets)? If not, a multi-sport helmet, while a little warmer on the river, also works for skiing, snowboarding, and bicycling:
$99 original, $65 on STP, $50-ish if you enter key code SITECOOL813 on an order over $100. 1 pound 3 ounces.
I was in a climbing shop a few months and was impressed by:
at 165 grams, it seemed to float out of my hands. It passes all the UIAA tests. Maybe there is / will be a similar offering styled for white water. $110 at REI. Or, if you prefer, only $303/pound. That's cheaper than silver bullion.