What period are you talking about?
In most cases, periphery states won't have HPGs - maybe one at the capital or other significant industrialised world. The rest have to cope with pony express - messages carried by JumpShip.
The ComStar handbook goes into more detail, IIRC - Inner Sphere worlds have class A, B and C facilities. Class C bundles messages together and sends once a week, B class more frequently, A more frequently again.
And, for most of the time from 3rd SW to Clan Invasion, that's how it was. At the time of the 4th War, the FedSuns & Lyrans had their "black boxes" (see also the Warrior Trilogy novels) in limited use. They had low bandwidth, slow speed, but - as you're looking for - evaded ComStar scrutiny. By the time of the Clan Invasion the DCMS had their own, but these remained very black, top secret things.
The secularisation of ComStar led to easier access to HPG technology, and - albeit not necessarily satisfying to most of us - the use of Black Boxes faded into the background. By the time of the Dark Age and Black Tuesday (correct day?), they seem to have been forgotten.
So periphery worlds - pony express is your best bet.
My two M-bills,
W.