Much of this decision hinges on whether we think Sypha is more likely to be currently held in an unsavory part of civilization or out in the wilderness. If she is being kept in a basement somewhere, Kopoi is likely the best choice for working out which basement and that is a situation where Robin's skills will be of limited utility in terms of actually locating our quarry. If the inverse is true, Kopoi at least understands enough about stealth to be of some use in the wild. On the basis of who is most likely to be useful regardless of the circumstances of Sypha's captivity, Kopoi seems the best choice.
On the other hand, Kopoi seems to have something of a personality clash with Ryza, and given that the two of them must learn to work together well enough to deal with a presumably greater force and rescue a hostage, having that kind of tension might cause the mission to fail entirely. Robin is a complete unknown, but I think Artemis knows Ryza well enough by now that if she says the two will get along, that assessment is most likely accurate. I share your concerns regarding how well he might be able to adapt should Sypha be held somewhere with more buildings than trees, but in this case I think the morale benefits of not having to deal with Kopoi's... eccentricities outweigh that particular potential issue.
On the other other hand, playing the meta angle, Phoebe wouldn't be offered by the GM if she didn't have something useful to offer to this search. I doubt it's that she's a better fighter than the two who are acknowledged masters of their field: she said herself that she's not as strong or experienced as the others. The established rapport is nice, but doesn't quite seem like enough to warrant competing directly with two trained professionals. So there's definitely something there that's intended to make up the deficit, and if we can work out what that is, that might be worth considering. Unfortunately we haven't been able to work out what that'd be yet, unless maybe there's an existing sense of "women aren't as dangerous as men" going around that might cause our enemies to overlook and underestimate us?
Ugh, we're a bit deadlocked at the moment. If anyone sees a flaw in any of our logic, we'd love to hear it, since we've got two obviously good options with pros and cons, and one option that looks like an obviously wrong pick but can't be because why offer a choice that is directly inferior to the other options? We're clearly missing something and none of us have been able to work out what yet.