The trouble with using one mini for the entirety of the DC universe is how dissimilar the various spin-off cartoon shows and films can be from the main continuity - to the extent of almost being within their own stand-alone universes. The Teen Titans cartoon is strikingly different from the various Teen Titan comic book incarnations (especially this most recent one, but that is a disgruntled rant that has no place here.) The DCAU Batman is a far cry from the Brave and the Bold Batman, and so on and so forth.

A few possible paths you could go:

1) Use just one mini type for the entire DC universe. Every mini from a continuum outside of the main DCVerse would follow the rules for spin-off continuum minis like Torchwood; that is, they can't move in a straight line.

2) Use just one mini type for the entire DC universe, but vary them slightly depending on which continuum they're from. The vanilla DC mini would look exactly like its larger counterpart, the DCAU mini would look like it had been drawn by Bruce Timm, the Teen Titans mini would be anime-esque, and so forth. A good middle ground, in my personal opinion.

Possible minis for these first two paths: mini-Monitors (http://dc.wikia.com/wiki/Monitors), mini-Oans (http://dc.wikia.com/wiki/Oans), Generic (Grey) Lantern power batteries.

3) Each spin-off with its own established continuity has its own mini. The DC comics, the DCAU, Teen Titans, Young Justice, Batman Brave and the Bold, and so on. This method is messier, but it does a better job of capturing the flavor of each universe.

Possible Teen Titans minis: mini-Silkies, mini-Cinderblocks, mini-Plasmuses (Plasmii?)

But I'm just spitballing here. Do whatever you think would be best.