Honest answer? I would not do both. I would also not be teaching her SAR with someone who is not an active member of a SAR team.
I am guessing by what you wrote that you want to do tracking/trailing? Not airscent? Have you found a team? Are you going to trainings? Are you learning everything YOU need to be part of a SAR team?
SAR is not a fair weather game. SAR is all temps. And honestly hot humid weather is harder for a dog because of how scent moves.
SAR is looking for people that are often odd and disoriented. Strangers, who may strike out, scream, kick at the dog.
Most, not all, reputable SAR teams will not allow a protection trained dog.
I have looked for SAR teams near me. The same result as SCH near me. Two hour drive minimum. This guy trains police, and security dogs, for departments and businesses all over the US. He knows his stuff. I have to pay a premium but driving 30 minutes compared to 2 + hours is a trade off I am willing to do.
The way it was explained to me is that tracking/trailing dogs can also be trained or will utilize air scents also but if a dog is trained in air scent it is harder to also teach tracking.
What my intentions are is to be tool for LEO's. A certified volunteer
Say little johnny wanders off in the woods cant find him, we get called in to help find him. Alzheimers patient wanders off gets lost, maybe we get called in to help find. I have talked to numerous LEO's and firemen in towns around me. They all say the same thing. Yeah, they would like to have a handler and dog available if needed.
I understand that it is an all weather deal but if moisture in the human capillaries or whatever the heck our scent is released with freezes it is harder for the dogs to keep a scent. He wanted to start off and set her up for success and work her into more difficult situations.
As far as people kicking, screaming, etc... I figured she would be on a long line with harness not free roaming. maybe I am mistaken on that. Maybe different circumstances will dictate that.
And finally shouldn't a proper trained bite dog only be in that mode when I tell her to be. Or only in certain situations. If we never bite on a trail and SAR is a totally separate deal then bite shouldn't be an issue.
Don't want you or anyone else to think that I don't want feed back or opinions just laying my thoughts out to see if I am crazy or if its even kind of logical.