I'm not sure anyone actually knows the real answer of how long it take for a virus (assuming all viruses are the same) to die, as it would require some in depth lab work. I don't fret too much about possible virus spread that I can't really control. My next door neighbor has a bed of 50 Lilium lancifolium that are sure virus carriers, but it doesn't seem to cause much problem. On the other hand, I do have several pairs of pruners so I can minimize possible virus spread when cutting different live stems, as cut flowers, for instance. This way I don't need to bother with disinfecting the pruners. (Also, I am constantly misplacing them, so I need multiple pairs.
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Rather than tearing the dead stems, you might consider pulling them instead. I don't get dead leaves flying off anywhere. There are advantages and disadvantages to this method, and I don't really advocate pulling over cutting (or vice versa), except perhaps in specific cases. There is a bit of a learning curve the the process, the object being to quickly snap the stem from the bulb in one yank, but not necessarily pulling the stem out of the ground with that initial jerk.
