I feel your pain, I have short arms and smooth tiny girl hands so grip in the deadlift is normally a big issue for me too.
As opposed to tacking on something at the end of the cycle, I’d implement some grip work as accessory on a day other than deadlift day. (I suggest not the days immediately before or after.) Doing it this way would make it a consistent part of your training and your benefit wouldn’t just be limited to doing it one week out of the month. You could spread it out more, be fresher and train harder with it if you let it spread over the whole four weeks.
There are a lot of great grip exercises to choose from, this article from Andy Bolton has a lot of great ideas, and from an obviously trustworthy source. There are a few other grip articles around the site, but this was one of my favourites.
Personally for me, what helped me the most was High-Rep Dumbbell Rows (Kroc Rows). Grip being your concern, and not so much back strength, I’d lower the weight appropriately down so you can hit a good 25-30+ reps on a top set and have your hands take most of the work. I schedule it in on Bench day to counter-act the whole push-pull equilibrium, and it’s a couple days out from deadlift day so it doesn’t interfere with my recovery. At the very least it’s worth adding in for a few cycles to see if it makes a difference, and replacing it with something else if it doesn’t.
Hope this helps, good training!