Percents are dimensionless already as Hoosier pointed out and it's fairly simple to work with nicotine strength like that.
N1 = Nicotine % of your unflavored nicotine liquid (50mg/ml = 5% (well, actually 5.05%))
N2 = Target nicotine % of final liquid
P = Proportion of final liquid that needs to be the unflavored nicotine liquid
P = N2/N1
Is that what you were looking for?
There is no need to really convert it, though. You could just do target 20mg / nicquid 50mg = 0.4 so you need 40% of the final mixture to be the 50mg liquid.