I was asked very recently about vegan, cruelty-free ink pads; my reply is, that unfortunately currently I have no proper information on any. Ages ago, maybe 10 years by now, Tsukineko wrote me that their pads were free of animal derivatives; to claim they are so now would be speculation. I did write to the company again for this website in 2017, but the company declined to reply.
BUT, even if I have no ink pads to show , I can tell you what I, and probably some of you have done, too. I used Faber Castell Pitt Artist brush pens to colour small stamps (not carved out of wood, that very well might hurt your precious supplies). Now there are the Faber Castell Albrecht Dürer Watercolor Marker; which have a thick juicy brush tip, meaning the stamp is quicker covered and you have more time to transfer onto paper, etc. before the ink dries. If they had time to properly dry on paper, before going over the colour with water, there will be only a translucent smudgy hue layer on top, but the line will stay put on paper; they also only activate once, a second slathering with water will not make line or the translucent hue layer budge further; of course you can do the ol’ trick with any felt tip pencils, highlighters, also watercolour, gouache etc. . For transfer on fabrics, fabric paint in marker or paint-from-jar-on-actual-brush works too. The latter very well. Liquid color applied to a kitchen sponge, or square cellulose sponge cloth or even a plate might also do the trick as ink pad substitute. In 2017, I received the information that gelli plates (Gelli Arts) are free of animal derivatives; theoretically, you might be able to apply liquid colours onto one of those and press your stamp into it to get the paint on and then go to town transfering. If you have a gelli plate, maybe that will work.
All of these methods have a plus point, which is you can go very colouful. You can colour your stamp’s design’s elements in different colours, gradients, a colour pattern … no limits.
There are no boundaries, of course don’t go breaking your pens now for the sake of an ink pad replacement, that’s too far .
Until I stumble upon cruelty-free company produced animal derivative free ink pads: Get resourceful, McGuyver the crap out of your art supplies.