I was going to suggest rainhandler as well - because I'm a civil engineer and I think it's a neat idea - but not because I've ever actually seen it used (it is not a common product). However, I would not install on my own home if heavy snows or ice were a big concern.
I believe what you're looking for is a simple drip edge, similar to your picture. Do a quick search for "drip edge" or "drip flashing" and you'll find all kinds of products (many of which are likely available at your local home improvement store). Drip edges are often installed with a gutter system, but can be installed on their own as well. A drip edge is just a strip of metal or plastic that moves water droplets a short distance away from a building and then lets them fall straight down.
As you've shown in your picture, a drip edge will usually have a 45 degree bend at the end. This bend is what makes the water droplets fall down, as it is very difficult for them to travel "back up" the backside of the bend. If your flashing were flat on the bottom I.e. a 90 degree bend, then it would not work well because water droplets could wick back to the building by traveling along the flat bottom.
One problem that I see with your picture is the placement of the flashing - there's no overlap from the metal roof to the drip edge. Drip edges are more commonly installed at the top edge (top of the fascia), often under shingles. The idea is that you want water droplets to roll off the shingles or metal, onto the drip edge, and then down to the ground. In your picture, water droplets would roll off the metal roof, down the fascia, and then (hopefully) down the drip edge. I say hopefully because most likely you'll end up with some sort of gap (however small) between your drip edge and the fascia. This little gap is where mold likes to grow and water likes to sit to rot away your fascia. Installing your drip edge at the bottom is fine, but I would then choose a product that covers the fascia too, and then goes up under the metal roof (the drip edge needs to somehow start underneath the metal roof). You want a continuous path of overlapped materials for water droplets to flow down - like how shingles always overlap the next one below.
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