I doubt if the grounds will make much difference, as long as you use one of
them. You can do a quick eyeball on it to see where they lead. If they
both go to the same trace, it won't make much difference.
Murphy's law is always in effect on sound cards. I've always had to rewire
the CD-ROM audio connector for every sound card I've put in. The last
couple times, I did it with everything "hot", just touching the wires until
the right channel came out of the right speaker. The common (ground) is
usually a dead giveaway you can find by visual inspection. Be careful,
don't touch ANYTHING else if you try this.