Hi I use the peel and stick tabs you use for hanging pictures. You can get them at Wal Mart. They work quite well. You may want to put one on each side of the top of the picture your hanging.
I always make a frame for my cuttings and attach the hanger to the frame. You can get 1/4" screws to fasten your hangers. You may have to drill the holes in the hangers somewhat larger for the screws to go through. You could fasten a short screw to each side and run fishing line or wire between the screws.
I also couldn't find nail short enough for the 1/4 ply so I take wire cutters and cut off a bit, I then use a little epoxy glue to be sure the hanger will stay in place.
I buy very small screws from Lee Valley here in Ottawa. They are meant for small hinges on jewelry boxes I think. A bag of 100 is only a few bucks. I usually buy the normal saw tooth hangers from Home depot and replace the nails with my screws. James
I buy the saw tooth hangers from Lee Valley you get 100 hangers for under 12.00 bucks its better than buying 4 or 6 for 2.99 from any wheres else i then drill the holes a bit wider then use the small screws also from lee valley tools i use a different size depending on the thickness of the wood going the little extra mile makes the overall appearance more appealing to the customer
I use the "hammer in" saw tooth hangers. Most of the time i bend the "nail" part out about half way down on both sides. Then I make a depression the width of the whole hanger and put a spot of epoxy on both ends and set the hanger in. I have also shortened the "nail" part with a side cutter and pounded it in. Sandie