PNG is better than BMP in my work and I too often forgot to change the file type before clicking save.
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There is no easy tweak for this to my knowledge. There is, however, the old trick to opening it with a blank file by default. Create a small blank PNG file and place it somewhere that won't get deleted, such as the system32 folder.
Open your mspaint shortcut and change the target to open this PNG as an argument to the mspaint executable.
Everything that's pasted into a new paint window will be saved in PNG format by default.
Don't forget to make this blank PNG read only to avoid saving over it each time accidentally ;)