First of all, great animation! The whale surfacing and swallowing the cow gave me a good laugh, it's always good to see Anim8or used for actual animation and you've obviously good a good eye for comedic timing. Unfortunately I have to agree with previous responders, ain't no easy way to do this in Anim8or. My personal preference is to keep the figure and paddle separate, as davdud101 suggests, however I would animate the paddle first, then animate the figure to suit.
Animating the paddle on it's own in Scene mode is relatively easy, you can get a pretty good paddle action happening with relatively few keyframes. Animating your figure's arms is obviously much more difficult as it involves at least three joints per arm (shoulder, elbow and wrist), two of which are 3-axis joints, giving 14 separate parameters that need to be animated. With the paddle already animated this job becomes a bit easier, as the paddle provides a positioning reference for the hands (this would be a LOT easier with inverse kinematics... hopefully this will be completed and enabled in future versions). Keeping the paddle as a separate Scene element also allows you to treat it separately from the figure, for example if you want your figure to let go of an object.
The test animation below was done this way, however I added one extra step that made things much easier. After animating the paddle and matching the figure's hands to it every 12 frames or thereabouts, I removed all the paddle's keyframes and re-animated it to suit the hands, with keyframes in every 6th frame. As mentioned, it was obviously much easier to animate the paddle in so many keyframes than all 14 figure parameters, and it allowed a close(ish) match between paddle and hands. So in effect, the paddle coarsely defined the motion of the arms & hands, and the arms & hands then closely defined the motion of the paddle.
To ensure all the figure's bones are available to animate in Scene mode, I added a single-frame T-pose sequence in the first frame (I left it in but this would normally be edited out). A second single-frame sequence with relaxed arms was added towards the end, after the paddle is dropped. All animation in between is done in Scene mode rather than sequences, this is very tedious but it does give precise control. It's worth spending the time, though you'll want to plan your animation well because once you have a lot of keyframes it's not so easy to move things about.
NOTE: This animation is far from perfect but hopefully it demonstrates what I'm talking about. The figure ("Eraser Man") is from a previous animation I did some years ago, it's about time he got off his backside and actually did something, the lazy little blighter...!
