Take a different example, take davaning. If you are in a public place and you have to daven before you miss the zman, than yes, daven. Its advised that you go to a corner and daven, not just start davaning in middle a everything, but to go to a telephone booth to daven, cuz you dont want to make a ‘chilul HaShem’ than i think that shows that the person is embarrassed. I think its the same with the tzitzis, amusing that you are on that level, and its something that you always do, than it would seem that you are embarrassed if you tuck them in, in no way is it a chillul HaShem!
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