Starfleet could have easily find someone in Intelligence and familiarize that person in conducting theta band carrier waves . . . or find someone in Intelligence who was familiar with this.
In the limited time frame to prevent an operational bioweapon being deployed? Maybe not. Jellico keeps saying the mission is time sensitive, & that's likely why. They've only been detecting the theta band waves for some weeks. Had they actually been in use, it might've taken someone with "Extensive experience", to deal with it, that a few short weeks training might not offer. (Granted, we never find out
what expertise he has)
Basically, the whole theta band delivery system was a ploy, specifically fabricated to draw out Picard personally, by Cardassians who'd learned of Picard's invasion assignments. It makes sense they could dig up
something, he's solely outfitted to troubleshoot, if they looked hard enough, & acted on, such to leave Starfleet no option but to turn to Picard in a rush. That was their specific goal
The only fishy issue is how Command is so gullible as to overlook the obvious trap, where only one guy is suspiciously capable, or did they in fact expect it might be, but because it was so potentially dangerous, if true, they decided it was worth the risk/loss?
Also, all the other members of the infiltration team happened be starring in the same TV series.
Admittedly, that's a harder bit to swallow, but there's nothing to refute Picard possibly choosing his own crew, of only 2 people, & wouldn't it make sense, from his view, to use 2 he has experience with?
It's illegal, so maybe they demand the team be as small as possible, a tactical & medical operative (Bioweapon)
Worf's a solid choice on any op, & Crusher maybe not so much, but she is likely qualified, & what might matter most to him is he knows & trusts their instincts.
It's interesting he says
one of the reasons. So, another reason still could have been some backstabbing Admiral who wanted to get rid of Jean-Luc
Maybe just another reference to Picard somehow being already assigned to handle this area of potential Cardassian infiltration, just like Minos Korva, both being near the border on opposite sides