"Призупиняти" is better than "Зупиняти", because it conveys that the music will be resumed. But if we change "при записуванні" ("while recording") to "під час запису" (~ "at the time of [making] a record"), the translation will be both accurate and easier to read, without overflowing. And the negated option would look like "Не зупиняти музику під час запису."