There are alcohol swabs with more or less alcohol on them, depending on which brand you use.
It's better to use a saturated alcohol pad before injecting, and a non-saturated one after injecting. The saturated alcohol pads are enough to encourage the bleeding, whereas the non-saturated ones are just fine to use IME.
Since this is could have been discussed in other threads, and because it got derailed, I'm going to close it.