Tzitzis

Question

I am designing a tzitzis beged and would like to have all four corners of the beged secured to the beged with snaps or with a zipper. This will allow one to remove the corners which are housing the tzitzis strings and wash the beged. It will also allow one to have many begeds and one set of corners. Are there any halachic issues that are at hand and if there are, is there any way to work around them? Yitz