I've yet to encounter in climbing a single situation where a pull-up bar scenario has arisen. If anything this workout is just a bad idea for a number of reasons. First, it causes significant damage to the elbows when done in the kind of numbers you need to make a diference. Second, it actually works out muscle groups you don't really need which contribute to a nice physique but superfluous muscle weight. The solution is to get yourself a finger board. Or build a campus board. Both of these will give you close to real life scenarios that you will encounter in your climbs. Now, not everyone can smear their walls with slabs of wood or nail a fingerboard up. So what can you possibly do for your shoulders? Homemade Climber to the rescue.
The picture to the right is taken of the inner part of your standard door frame. As you can see a thin strip of wood lining the inside of the door frame makes for an interesting crimper simulation. However it only offers you sideways and upside down angles. No worries. Try standing perpendicular to your door frame and holding the crimp with one arm step right next to your door frame and lean outwards. In this position you will be able to repeatedly pull your body weight into the door. One week of this and you will be a monster at shoulder strength.
Another good exercise with this part of your door is to stand about half a meter from your open door. place your fingers in the crimp with your hands facing out. This will feel weird. But lean into the door until you feel that the weight is being held by your shoulders. Lock off in intervals of 15 seconds. Rest about 1 minute between sets.
If you keep a regular training schedule adding these two to your roster should give you noticeably increased shoulder strength within a week.