Increasing rigidity of curved, long, thin parts
The flexibility of 3d plastics has a lot to do with the additives manufacturers use.  The same base material with additive X may have very different properties than the one with additive Y.

That said, generally speaking PLA is known to be more rigid (and brittle) than ABS, but less strong.  So: you have a fair chance at giving it a go with PLA, albeit you my end up with a more delicate object in the end.

There is a well known youtube channel, whose author has performed a lot of quasi-scientific testing on common brands of filament (PLA and not) where you can get an idea of the relative rigidity of the filaments.  You can find the table with the results here (look for the "bend test" columns).

However the very firs thing that came to mind when reading your post, is that you could simply swap pins and holes by putting the holding pins on the arm, and the holes on the globe instead.  This would allow you to preserve your design and to have longer pins.

Things you could try when it comes to printing (unless you are already doing them):


Print the arm flat so that the layers stretch from pole to pole uninterrupted.
Print with near solid infill (solid infill can be problematic if your extrusion calibration is not perfect), like 95% and cubic infill (for more uniform properties along the full length of the axis.


Finally, you could try to anneal the arm in your kitchen oven.  This process works by warming the part until it becomes pliable and then letting it cool very slowly.  The end result is that the molecules arrange themselves in a more "crystal-like" way and the part becomes stronger and more rigid.  Beware that annealing changes your part dimensions so you should definitively do some experiments with a test cube and find out the direction and percentage of the shrinking before going "all out" on the arm.