To elaborate a bit on Sam's reply, in the USA, the copyright holder could, in principle, dispute your claim of a fair-use (ie, educational) exemption, but the probability of this happening is exceedingly small. The only worry is that should you (...I know you said that you wouldn't...) or someone else start selling some product based on your tweaked version, and it became a big hit, then, once the scent of money is in the air, the lawyers could try to see what they could extract from anyone involved in the production and distribution of the successful product.
This is not a hypothetical situation. Exactly this happened just a few years ago in a very famous case that involved an image of President Obama taken by an AP photographer, which was then modified by a graphic artist named Shepard Fairey, and the resultant image became very successful. There's a good introduction to this case on Wikipedia:
https://en.wikipedia.org/wiki/Barack_Obama_"Hope"_poster
But, as I said, the probability of this happening to any indvidual is very, very small.
Personally, I'm a belt-and-suspenders type of guy, so to avoid any chance of this happening, I always use either photos I have taken myself, or images in the public domain that have no copyright restrictions. There are websites that specialize in these.
HTH,
Tom M
PS - Sam's advice not to put your own watermark on your tweaked version of someone else's image is very sound. Doing that is tantamount to waving a red cape in front of a bull, LOL. Besides, would you like to see someone put their name on your photo?
