I use Clik Clak candy tins that are about 1.5" in diameter and about a half inch thick.  Mints and other flavored small candies come in these.  I can force in a large amount of vaseline/cotton and the lid clicks into place.  A push on the center of the lid...claks it open.  Neat, thin and hold plenty of cotton.
I add the vaseline to the cotton in these tins.  Lay in some vaseline, then a pulled out cotton ball, vaseline, another pulled out cotton ball, forcing it down hard.  Repeat...this forces out any excess vaseline and really packs the tin full.  

As to plastic straws I just cut them long, fold the end over, then secure the fold with a short section of straw.  I usually put a short string along the cotton as I force it in...then a gentle pull will remove a bit of cotton easily.