Really? Most of the no guns strat I've heard was on just using missiles after the Republic Frigate and no guns at all at that point.
Either way works. Once you're out of the middle of the minefield, you're more in danger of asteroid damage than anything else.
If you can dodge asteroids well, the 4 remaining ships don't do enough damage to overload your shields so you can let your guns blaze.
On the flipside, there are only 4 ships, so it is very easy to kill them exclusively with missiles and no guns at all.