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A simple fan will produce cool air at the centre of the flow, with hotter air at the periphery.
Small and efficient vortex tubes are used for cooling cutting tools. They cost less than $100 from China. (eBay "Small Vortex Tube Cooler SE-WLG08 Vortex Tube + Joint Universal Tube 4150")
Search eBay for "vortex tube" and you will find "Vortex Tube Air Conditioner Waistcoat Compressed Air Cooling" below $100.
A bicycle pump immediately produces hot air. You can use a vortex tube to increase that temperature.
If you want to produce cold air from a vortex tube, you will need an intercooler or storage reservoir to pre-cool the compressed air.
https://en.wikipedia.org/wiki/Vortex_tube