Paste the path info to mask path or a motion path, scale the mask or motion, copy & paste it to the hand or link the hand with a simple pickwhip expression. Motion paths can be scaled by selecting all keyframes and holding down Alt to trtansform the bounding box in teh comp viewer, masks can be scaled directly. You may wanrt to read the online help for further details.
If you have the path on a layer that has been scaled or moved, a better workflow would be to go to Window/Create Nulls from Paths script, select the path and choose Trace Path from the options. This will create a null that follows the path and a couple of keyframes to control the timing.
The next step would be to create a comp-sized solid layer and apply Write On to that layer.
You would also want to set the anchor point for the hand layer to the pen's point.
Now press P to reveal the position property of the Hand layer and the Null, spin down the Write On properties on the solid layer in the timeline so you can see Brush Position, and make sure that the Parent Link column is open (Shift + F4) and then use the pickwhip to tie the Brush Position to the Null's position, then the Hand Layer to the Nulls position. Then you're done.
You can scale or position the layer with the path all you want, and everything else will follow.
A better option than the Write On effect would be to use the Pen tool and a shape layer to trace the drawing, add Trim Paths, and then use the Create Nulls from Path script to trace the shape layer path. You'll get a better result without scaling anything. You can tie the position of the Pen point directly to the path and quickly animate the timing. You can even use the shape layer path as a track matte for the illustration and reveal the drawings as the pen passes over them.