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.