As regards to compression yes the skimming of the head WILL effect the the C/R of the engine.. the thickness of the skim will determine how much by.
You can just use a thicker Head gasket BUT the cometic ones are quite expensive!
a very slight skim of the head wont make too much difference to the CR and nothing internal will have to change..
the only difference that will be have to be made will be to your timing and possibly ignition map