Just like with the Drowned Hope quest, the design is to make you perform the entire walk to the Pump Station from St. Christopher's Church in one sitting. Thus, you can't simply take the quest early and then wait until Boat Supplies to pick up the toolbox. With Fast Travel you could still actually do this anyway which is probably why the Fast Travel turn-in bug (below) exists--so that you'll have to brave some parts of the streets.
Sometimes, if you fast travel, Bruno will not accept his toolbox, but will skip to the dialogue he says when you retrieve nails (Three Nails quest), such as "Oh, this will help, but if you find more then please, bring them back." This glitch can be fixed by entering a different area (i.e. Abandoned House in Moresby) and walking back to the church.