It is known that Shalom is a name of Hashem, thus it is forbidden to say it as salutation in some places. And also, to not write it in a letter, because the risk of the receiver throwing it to the bin.
But what with the English word "peace"?
(An example: to avoid thinking on Torah in the closets, I once tried to read in a fat historical book there, but this word was appearing at very high frequency! No far from every 2 pages...)
Problem is not because it is not Hebrew.
But, because the Hebrew word Shalom loads more than peace-as-opposited-to-war; also the root Sh-L-M makes reference to wholeness, integrity etc.