Could you make a custom stamp with just 3D printed plastic? Sure! Plenty of designs out there.
TL;DR I just wanted to play with silicone and fuse it with printed plastic:)
I was playing with silicone caulk to make mini figurines using 3D printed molds and thought that the cured silicone was pretty flexible. So as part of my further adventure in 3D printing I decided to combine silicone with 3D printing again. Given the silicone is flexible I thought I would make a great substitute for rubber part of stamps and hoped that the flexibility would mean that the ink transfer would be better than a hard potentially uneven plastic. Using the plastic as a negative mold also means potentially finer details (/slight more flexibility) but the silicone may be too flimsy by then.
I don't have any stamp pads so the image you see is a result of roughly coloring it in with a permanent marker then stamping. Looks decent imo.
Rather than design a whole new handle I just took the one designed by Pumpkinwaffle and modified it to suit. The handle requires support but you could remove the column for alignment to print without support