If having a one body part per day training workout, than training arm's on their own day, would be the only exception for an individual arm day. This one day/one body part has been around for quite a while. Usually 15 sets on any one body part (3 exercises of 5 sets each). Though this system can be done 6 training a week, with the calves and abs on the same day.
Like:
Chest
arms
legs
delts
back
calves/abs..optional workout day
Putting the legs, the heaviest compound movement, in the middle puts some space between the chest and back work, also heavy compound exercises. Better so if you include DL's in the back work.
Can't take the biceps out of any pulling exercise, not matter the grip. The bicep has a main pulling function, even the common BB curl is a pulling movement (biceps=pulling a weight towards the body. Triceps=pushing a weight away from the body). If injecting a nerve/muscle numbing compound into the bicep, any rows, chins, clean, etc would be very, very hard to accomplish..if at all. Even triceps work,with that numb bicep, would be demanding. The bicep and Tricep counter balance/support each other in any function.
The weakest link to hitting the lats/back, and building it to it's full potential, are the biceps and grip, with pulling exercises. They give out before the extremely powerful back can be properly taxed. In any event, keep the focus on the elbows and pull with them, rather having the attention on the position of the grip, when doing rows, chins, etc..Lead with the elbows.
A pullover type machine, with the elbows resting on pads, give a direct work curve to the lats/back, with the biceps (for the most part) taken out of the exercise. Main reason a Nautilus pullover(and some other type machines) machine is so effected for building the lats. The closest, where the elbows lead the exercise, is the bent arm or straight arm BB/DB pullover. Allowing for a full stretch at the bottom of he movement. There are elbow slings/webs, which some attach for a sitting cable row or even overhead pulley's and chins....though not too functional or easy to get adjusted. Good Luck.