[Space] Eccentricity

[David Johnston2]

So, I'm rolling up a star system. In theory it's supposed to have a conventional gas giant arrangement. In practice the binary companion (a red dwarf) is close enough that there's no actual room for any gas giants. The red dwarf is 6 AUs away at it's closest approach, which takes it inside the snow line, but the planet I'm concerned with orbits at 0.47 AUs

Here's the question. How eccentric should its orbit be? Should I treat it as if it was still a conventional gas giant arrangement, or should I ignore that?