You mention the inkjet printing option. I'll focus on that. In a nutshell, you'll be disappointed, although it might be an option if you lack the skill and instruments to do miniature printing by hand.
Inkjet printers can lay down microscopic droplets of ink at very high DPI, but you don't really have control at that level. They are designed to reproduce detail and color accurately down to the level you can readily see at a normal viewing distance. Below that scale, the ink droplets are used to create optical illusions to simulate what you think is there. The printer driver and printer electronics control all of that detail to create an approximation of what you ask it to print.
The tiny droplets are small enough to simulate smooth curves. If you're printing in color, a large mass of mixed-color droplets is used to approximate the actual color from primary colors. Color inaccuracies are compensated by making adjacent areas off-color. At the scale of the individual droplets, droplet positioning is pretty imprecise, and some randomness is thrown in to avoid creating neat geometric patterns that your eye could detect as artifacts.
To illustrate the limitations, I created a little text using a simple font at a size of 3 pt, and printed it on regular printer paper. Here is an enlargement (actual size is about 1 mm high:
At this scale, the ink wicking is significant relative to the size of the characters (although you could do better than this using photo paper). You can see the "wiskers" and bleeding into the small voids within the characters. You can see the aggregation of ink dots creating the character lines. At this size, it's difficult for the printer to accurately reproduce the character geometry. With normal 10 or 12 pt text, the characters would be large enough that these issues wouldn't be noticeable.
With good font selection and photo paper, you could create readable text at 3 pt., but you might want to use a magnifying glass to read it if you don't have perfect vision. It gets dicey as you go to smaller point sizes than that.
One benefit of inkjet over manual lettering is that it would be much faster. Miniature writing by hand is something done slowly and carefully under a magnifier. Also, you wouldn't risk spending a lot of time creating the miniature text and then accidentally ruin it with a stray mark. With its limitations on readability, it still might be perfectly adequate if the objective is just to create the appearance of text and readability isn't critical.