You can process your salmon wherever you want. You just need to leave the tail on one side of the fillet, make it clear that the other side goes with that piece (by bagging and labelling properly), and you need to make sure to leave the head on if it is close to too small for the area, or close to too big in slot areas.
Your halibut and lings can also be processed wherever. You need to leave the head and pectoral on a piece and label the rest. There are measurements in the regs for the size of a head-off lings and halis.
I find it simpler and get a better product on short trips if I dress my fish head on, store in well-drained salt ice, and fillet and vacuum when I get home. The tricky part is finding an open dumpster in town if I miss garbage day. The garden is all planted and we have bear aware signs in the neighbourhood so I don't want the heads and bones.