Surgical strikes can be handled by standard fighter wings. You only need SOC wings for covert surgical strikes akin to the fedayeen first mission.
Also I'm gonna go out on a limb here and say he SOC is friggen huge. The GTVA is a large polity, and certainly in BP canon, possesses a fairly restive populace. In addition to a capable fleet it would be sheer lunacy for the Tevs to keep the SOC tiny. Half the reason they are so elite and experienced is because they get blooded on subversion missions a lot, or at least that's what I read into them from the back story.
I have to assume they operate on a similar level to the GTI in pre GTVA time, allthough post Silent Threat probably with a lot more oversight. But considering GTI possessed not one, but two capital ships for their exclusive use, and those are just the ones we saw, with, I might add, a full scale GTI rebellion taking place. A revolt by a significant portion of your forces should put a significant dent in the number of ships you can field, yet they could still field two orions that we personally saw.
I think the insinuation that losing a few fighter wings and some transports would cripple or seriously harm the spaceborne operations of the SOC to be laughably far fetched. Fighters are replaceable, and more SOC pilots can be rotated in from out system.
On the topic of the transports - were they loaded with SOC operatives? Or run of the mill marines? I honestly don't remember, and I'm not in the position to do the checking right now (wrong computer), but from what I remember of the mission that doesn't seem like the job for transport upon transport of specialized operatives. Elite cadres of marines sure, with a few specialists on board, yeah I can buy that. But how hard is it to secure a station against hostile boarders or its current inhabitants? That's exactly what marines are trained for, I don't see why a standard force of Tev marines couldn't have been used for that purpose. Again, the Tevs are well practiced at putting out regional bush fires, I expect their marine core is suitably large, disciplined, and competent.
SOC operations don't need to be purely SOC shows, and standard fleet elements can often (and I would be surprised if they didn't) directly support those operations. You don't need to know what the objective was if your orders are just 'hold this stations' or 'cover these fighters'. The Fedayeen and the Fed fleet work together now and then, such as the attack on the carthage, I don't see why the SOC and he Tev fleet would not. Just because the SOC had a hand in some mission element doesn't mean that every asset destroyed was an SOC asset - it doesn't even mean most of them were.