<<< I choose some curve run the script by shortcut and in clipboard is saved length of selected curve.

Yes it's exactly this! :)
The value of the lenght of any curve(s) selected is pasted in the ClipBoard!
So if you have some NotPad open somewhere you can read it after copy the clipBoard inside! :)
Not very speedy but better than nothing! And very informative! :)

Another thing is existing! (maybe not very adapted to your case but...
CurveLengthBeingDrawn :)
http://kyticka.webzdarma.cz/3d/moi/#CurveLengthBeingDrawn

or on my page in French ;)
http://moiscript.weebly.com/curvelengthbeingdrawn.html