Several options, i'll start with the multi option path first.
1. use a weighted egg pattern. All you have to do is put a tungsten bead on the front or sometimes you can do a mcflyfoam egg around a tungsten bead.
2a. Fish like you have an indicator, only using your fly line to keep the fly off the bottom.
2b. Tightline the egg pattern by either high sticking or euro nymph strategies. Now I am assuming no line attachments are allowed (BC's definition of fly fishing). Make a leader using around 15lb Ultragreen, I think I have around 10 feet or so. Then from there I go to about 2 feet of .09mm Hanak bicolour indicator tippet (umpqua makes it as well, but 10lb gold stren will work just as well and is cheaper) which is known as a sighter. After that I have around 6-8 feet of 5x tippet. Now I use a 10' 3# designed for this type of fishing, but a 9' 6# will work but not as well. if you have a 5# or 4# in 9-10' it should work well. Note casting is a pain as it is sort of a lob cast. Cast upstream, allowing the sighter to touch the water. from here bring the line up to form a tightline with only the 6-8' of tippet in the water. Keep the rod tip ahead of the line and lead it through the water.
3. Use a non weighted egg pattern.
4. swing the fly using a sinking line
note this might cause accidental salmon snagging...