I'll admit, when I'm reading aloud from the page I may be inclined to purse my lips a bit before beginning the "wr" sound, but when speaking ad lib "wrap the present" I'm sure I don't; and I'm sure the listener couldn't detect the difference anyway.
I have no idea why, but many non-native speakers want to substitute a g for the w, saying grite, grap, grack, etc. Don't!!! Make yourself believe that the initial w is not