If you are in NYC and a clip is shown that alone gives the officer the power to stop you, and take it out as it is now in "plain view", which is legal for an officer to do as they are witnessing an individual carrying a knife on their person via the clip...
In NYC the laws make it very easy, as just about NO knife is legal to be carried, and even if the knife is legal (such as a swiss army knife) it HAS to be concealed in the pocket fully, not able to be seen at all, including a pocket clip. -- barring the legal utility use of said knife...one example being: you are in the park having a picnic and cutting an apple or other food.
If you are found to have a mini-grip on you, the mini-grip will be taken from you, and vouchered never to be seen again, and you will also be arrested for criminal poss. of a weapon or you will be issued a criminal court summons and given a date/time in which you'll have to appear in court before a judge to answer for it.
So to answer your question, no... It wouldn't be a good idea to clip your BM to your pocket... If you MUST carry it, carry deep inside your pocket and have NONE of it show... However bare in mind if you are ever searched (even not related to the knife that you carry) or arrested for anything (even not related to that knife) once they find the knife on your person, that will add an additional charge to what your already being charged with...