Without evaluating your information and you directly, it is hard for me to say exactly what needs to be done here. I find it very difficult to believe that “extremely mild” aortic regurgitation would be grounds enough to keep you from playing competitive basketball, or any competitive aerobic activity, for that matter. It is unclear to me whether you have a bicuspid aortic valve, in which the aortic valve has two functional leaflets. If this is so, then you are also at risk for progression of the aortic valve leak as well as obstruction of the valve (stenosis) and dilation of the aorta with potential aortic rupture. If these do demonstrate progression, we typically recommend that you not participate, at minimum, in sports that have a high “static,” or isometric, activity level, such as weightlifting, football, or wrestling. That said, I also find it difficult to believe that you have had complete resolution of the disease and the abnormality of the valve; bicuspid aortic valve does not resolve. I will say that trivial aortic valve regurgitation can be considered a normal finding in the face of a completely normal aortic valve, although I do not know whether you had this, or not.
Therefore, my recommendation is that you be evaluated by a pediatric cardiologist, if you can still see one at the age of 18, who can fully evaluate your valve and discuss these options with you. The other option is to obtain a second opinion from an adult cardiologist. If your heart is completely normal, you should not have any limitations on your athletic participation.
Finally, kayaking is felt to have among the highest components of both aerobic and isometric (dynamic and static) exercise, so I can’t say to which of running or bicycling it is closer. It is almost immaterial here, though, as it seems more important to have exactly what is going on with your heart defined first before deciding on participation in various types of sports.