Do not ever call any tower position while on the ground at a satellite. Approach control, maybe, but that's also usually a total waste of time, and most approach controls will not issue a squawk code to you for your VFR departure anyway.
Really? I must be a real cowboy then ... I get squawk codes on the ground and told to contact approach once airborne quite often if I'm heading into or transitioning our Class C. I usually do it via CD and EXPLAIN IT sometimes being told to contact APP directly. Also, I can explain that I can't accept their 190 vectors over Mexico (new crew at tower loves pushing small tin over Juarez MX as they have an LOA over there) due to insurance and firearm on board.
There was a pilot who got in trouble for doing something similar in Florida around 2010. He called Ground Control at the primary airport, claimed that this justified the initial contact required by Part 91 before entering Class C airspace, and then departed from a satellite airport and climbed into the primary airport's departure corridor on a 1200 code. Does anyone remember this story?
Well, yeah that was stupid ...
1. Obtain squawk
2. Depart get off CTAF as soon as practical and contact approach
3. They respond and voila ... smooth
-- VERSUS --
1. You: Tiger 12345 Request
2. APP: Tiger 12345 say request
3. Tiger 12345 VFR over Sunland Park 5500 climbing 9500 transition over downtown request advisories, destination KEDC Austin with Xray
4. APP: Squawk 4123 and ident
5. APP: Tiger 12345 Radar contact 2 miles from Sunland 7000, turn heading 190 for now
6. You: Tiger 12345 unable 190 vector, request any other vector-altitude that excludes Mexican airspace
7. APP: Tiger turn 190 for now, need to work something out
8. APP: Tiger 12345 descend to 5500 and follow the river