Splicing line to pull lines out of rigging for cleaning

I've gotten advice that the lines in my rigging seem to be in good shape but that I should clean them and that one way to do that would be to splice another line or some sort of cord onto the end and then pull the line through and off for cleaning, leaving then, the other line or cord to then put the clean line back on and pull through the mast.

Is anyone experienced with doing this (and avoiding getting things hung up, etc.) and willing to come down to my boat and help get me started on it? Free pizza and beverage or ....whatever works for you! :) I'm thinking of doing this mid-April (after Folk Festival), but could maybe do it this weekend (March 28-29-30), if the weather isn't too rainy.