Wowwie.. 1/4" is a big leak and not particulary high velocity nor an accurately aimed jet of cooling air.
If you terminate that 1/4" line with a threaded fitting, you can experiment with various line/tubing fittings to make an adapter for a more suitable tip which will enable you to direct a fine blast more effectively.
The cutting tool is already twirling around in air, so it's essentially fanning itself. The aluminum workpiece is sinking away heat from the tiny contact area being cut.
So, I believe the most benefit that can be attained from an accurately aimed blast of air, would be chip evacuation, and not so much a cooling method.
The energy cost and wear of the air compressor would be significant with a
1/4" orifice/air blast. Getting the hole size down into the decimal range under 1/16" would probably be effective.. possibly two small blasts depending upon how the table traverses, so that a path is also kept clear ahead of the cutting tool.
You can experiment with various tip shapes without needing to get too technically involved into concentrating a pinpoint blast, which is basically the opposite of most commercially available sprayer tips for various fluids. Tiny tubing can be gotten from aerosol products that supply those extension wands for squirting the stuff into confined areas.
A tiny orifice hole with a tapered hole behind it, to accept an adjustable needle valve/screw may be all that's actually needed. How deep the straight hole is (beyond the tip of the needle point) will likely be the determining factor for the shape or concentration of the air blast.. WAG.
Testing air streams ain't so easy, but some sawdust may be helpful to see what's taking place. You may find that 40-80 psi will be very effective with small orifice sizes.
A smear of cutting lubricant may still be effective, as long as it isn't making the fine chips stick to the workpiece.
I'd suspect that recutting chips would be far more detrimental to performance than heat generated by the cutting tool.. JMG - just my guess, you'll be the best judge of that based upon what you can see.