Before you jump all over me about code violations, let me preface this by explaining that this is a house in the Caribbean and what plumbing there is would never pass code in the US or elsewhere (and don't ask me about the electric!).

The shower is installed without a P-trap below the drain. It ties into the sink waste and then runs outside a short distance into the ground where it enters the septic tank. The toilet waste line is separate from the shower and sink line. And not surprisingly I'm getting bad smells coming from the shower, since I'm assuming that it's just letting the septic gasses come back up the line when the pressures are right.

My question is: can I just cut into the shower/sink waste line outside and install a trap inline? If so, what type of trap, and does it need to go between the fixtures and the vent?

It seems like this would do the same job as a trap directly below the shower, but I'm hardly an expert, so that's why I'm asking you folks!

Thanks for any help.

The trap you are talking about is called a "running trap". Depending on the size you need it will be from about 18 inches to two foot long. Actually it should b installed out in the yard and it would be very easy to install, just cut out a length of pipe equal to the length of the trap plus about 1/2 to 3/4 inch. Then use a rubber no hub clamp on each end to seal the pipe and the trap together.
This trap will do exactly what the trap below the shower will do with one exception, the running trap out in the yard will stop the gas from rising out of the septic tank and up through the vents on top of your house. That is the biggest complaint we have and the main reason we install running traps.