Small high-power LED flashlight with focusing control can project a small patch of light up to a few feet away. Cheap ones are available for as low as $5-$10.
However, white tint varies so depends on your specific needs; for display purposes, quality may or may not be up to what you want. Light patch can have artifacts such as bluish at the edges. Tightest focused patch appears as a lighted image of the LED die itself; you might even see the bond wires!
Some flashlights will project a light patch larger than you want. One I tried did a patch about 1.5" square(ish) at about two feet, the other at only one foot. Not quite tight enough for these.
Another concern would be running continuously for long periods of time, especially high power e.g. 4-5W. Flashlights are generally not meant for this. Most have medium and low settings which are set manually.
You would probably to wire to a dc power supply, no higher than 5v for light designed to run on 3AAA cells or single Lithium-ion; better a bit lower, not hard to do. A 5vdc 1.5A wall adapter with 1-2 diodes in series should work.
I can't think of anything else in common usage with a beam this narrow. There are display lights specifically for your purpose, but no doubt higher cost.
Dave