Anyone whose had lymph nodes out is at risk of developing lymphoedema, and as someone who has it, I can tell you it is a GIANT pain in the neck, uncomfortable and mentally difficult to bear. Because you've had your lymph nodes out it will be more difficult for your arm to shift the lymph than for a normal person. That is why the booklets tell you to take precautions against breaking the skin on you at risk arm.
So as well as the weight of the fatties (LOL), there is also the repetitive strain of the brushing and, perhaps most important: the increased risk of dog scratches and or bites. There are several women on the breastcancer.org website who developed lymphoedema after more than three years, so I wonder about that research--who did the study? But I know women who weightlift and row with no problems even though they HAVE lymphoedema, and the University of Pennsylvania did a study on a rather large group of woman showing if they worked at building up their strength slowly they could do heavy lifting without exacerbating lymphoedema, although they couldn't show it prevented lymphoedema.
Perhaps the biggest worry would be that if you developed lymphoedema you might have to, once again, change profession--so I think it might boil down to how much you want to do it. If it seems like your dream job, you may be willing to run the risk--after all, you might never get lymphoedema. It also might be possible to wear protective clothing, or make yourself less biteable/scratchable. On the other hand, if it's one of several things you are considering, the risks might make it not worth the effort.
Good luck with your decision.