I think it's relatively safe for us to go on missions. What we need to do is travel on skywalkers and camp on skytowers, and not route our mission selection through Tower bureaucracy. This fully shuts down any way anyone would have to track us, unless they're Hidan and just always know where you are at all times. (And even then, Hidan's busy)
And the thing about Seventh Path combat is, well, it's almost certainly going to be against other sapient beings. Hazou helping out in Dog likely means fighting Hyenas, and we know Kei will soon be forced to do the same. I don't know who the Toads get into scraps with but it's almost certainly another Clan. Personally, I'm not really torn up at the idea of Hazou fighting and killing a Hyena who's trying to raid Dog, but killing chakra beasts actively helps the people of Fire so I think Hazou and the rest of Team Uplift would prefer a chakra beast mission over a Seventh Path mission. Sage knows Kei's gonna have enough Hyena blood on her hands soon enough.
(Oh, and also, it's a lot less sus on the Jashinism question if we want to go kill non-sapients that definitely do not count, in contrast to suddenly chomping at the bit to go kill sapient beings like members of the summon clans)
Mostly though, it's just a plot hook opener. If the QMs have a cool combat sidequest to toss our way, we're set. If not, we'll probably just get vague assent from Kei and Noburi and then we'd get initiative tossed back to us and we'd get to add more detail based on what they said.
I'm not sure that this would be very useful to have, because the things we're asking for can't be easily renewed like that. It'd turn into "renegotiate after a year" as we decide on a new price anyways, so there's no real value in trying to automate it here.