Absolutely this is a liability problem for the club and its officers. If someone were injured by a dogbite at an event, there is a significant risk that the injured person would sue not only the dog owner, but the club and all individuals responsible for organizing the event. This could include all club officers and the trip leader(s), as well as the club itself.
Further, when someone sues, they don’t necessarily investigate beforehand whether the defendants have any assets. It is very easy to name an additional defendant, and a club organizing an event is someone that would undoubtedly added to the suit. Also, depending on state law, the members and/or officers may have some liability for the debts of an unincorporated organization.
It seems to me that, as Muffin mentioned, you have a much bigger risk than dogbite. Paddling/kayaking is an adventure sport and as such contains the risk of injury or even death for its participants. Most boaters (I’m one) know of the risks and understand the possibility of coming out of the day scraped up or much, much worse. Further, even the most skilled and safe paddlers face the risk of having something happen due to something stupid done by their fellow boaters.
If someone is seriously injured while paddling, there is a good likelihood that they will sue the trip organizers, including the club and its officers and trip leaders. Even if the trip is well and safely lead, the fact that some people on the water can (will) do stupid and dangerous things puts everyone at risk. And looked at in hindsight, particularly through the lens of litigation, there will always be “what if” things that the trip organizers will be faulted for.
As such, it is important to consider liability issues and insurance in any sort of club activity. Directors and officers insurance protects club leaders from being personally sued for the club leadership decision making they are involved in, but does not protect the club against being held liable, and it will probably not protect individuals against liability for things they actually personally participated in while on the trip. What you really need is a comprehensive general liability policy.
I would look at having a comprehensive review of your whole liability situation. Waivers may be helpful as a defense somewhere down the line if you get sued, but they won’t prevent you from getting sued. Merely getting sued is a very expensive and unpleasant process, particularly if you do not have insurance. One of the most important features of insurance is that it pays for a legal defense of a claim, not only pays the damages if you are liable. Also, unless you are exceedingly compulsive about waivers, it is likely that if an incident happens, the member or guest injured will be somebody who hasn’t signed the waiver or whose waiver was misplaced.
Finally, even a member who is the greatest fan of the club and who you believe would never sue can easily change their tune once they are injured. Further, even if they intend seek to sue only the dog owner, once they engage a lawyer it is highly likely that the lawyer will strongly recommend or insist on suing all potentially liable parties, including the club and possibly the officers, trip leaders, and perhaps general membership. If, in the worst case, a death occurs, the survivors will undoubtedly not retain any good feeling toward the club and its leaders.
Unfortunately, where there is a serious injury in an adventure sport like paddling, litigation may often ensue. Although the doctrine of assumption of risk, particularly if there is a waiver, might prevent ultimate liability, it won’t avoid the risk that the club and its officers and members get embroiled in a lawsuit.