In reply to SARS: Hey mate, hope I can help. Excuse me in advance if I seem like a know it all.
Firstly, you said you weren't going to do back exercises because your back is covered by climbing. Well, it isn't. Unless your back is already so strong that you're campusing up the wall (I'm guessing not) or your technique is so bad that you're still relying on back strength to haul your way up (I sincerely hope not), a climbing session isn't enough to get a great back workout. Add in a vertical pull like pull ups and a horizontal pull (row variation). Something you can do to allow a fair amount of rest between sets without taking too much time is supersets. For example, if you were to superset your shoulder press with pull ups, you'd perform one set of presses, one set of pulls, then repeat until you're done all the sets you had planned.
Secondly, you said there was no leg work as you're doing "quite a lot of swimming". You then said you were swimming just one a week. Well, people saying "I don't want to train legs because I do swimming/jogging/morris dancing" is the oldest excuse in the book for not training legs and has little merit to it. A cardio vascular activity like swimming does not train the legs in the same way as a strength based/anaerobic activity like a weight lifting workout. You don't need to train legs like a body builder or a power lifter might (although squats and Deadlifts wouldn't hurt) but at the very least throw some Bulgarian split squats and kettlebell swings in there.
Thirdly, the main thing that climbing needs is a strong grip. So train it! Two climbing sessions and two world that include a little grip work won't be overtraining if that's your concern. Buy a pair of Fat Gripz or similar product and use them on dumbbell and barbell handles for just about every exercise, whether it's a push or a pull. If you absolutely must then simply wrapping some towels/flannels around the handles will challenge your hands. You can also incorporate some direct grip work like farmer's walks, plate pinching or heavy finger rolls.
Fourthly, your core is made up of muscles, so train it like any other group of muscles. Don't waste your time with 100 crunches. Just because you feel a burn doesn't mean it's effective. Try doing standing cable crunches with enough weight that only allows 5-10 reps a set. Look up an exercise called 'full contact twist'. Try hanging leg raises. Do big challenging movements with as much added weight as needed to keep the reps fairly low.
Finally, ditch most of those isolation exercises. I'm not anti isolation and they have their place, but right now since you're only training twice a week for an hour each time, you need exercises which will give you the most bang for your buck. Here's a sample workout (yes, I can get a little geeky once I'm on a roll...)
A1 dumbbell shoulder press 3x5-8
A2 chin up 3x5-8
B1 Bulgarian split squats 4x5 (each side)
B2 kettlebell swings 4x15-25
C1 one arm dumbbell bench 3x5-8
C2 one arm dumbbell row 3x5-8
D cable crunches or hanging leg raises 3x6-10
E farmer's walks (dumbbells with thick handles) 4x20 seconds
1 minute should be enough rest between sets. You don't have to do this exact workout, but I hope it gives you some food for thought and I hope this rambling post has been helpful.