You can quilt any way you choose. SID is not the only choice! Our guild has an opportunity quilt (fund raiser) that is log cabin and applique. The gal that quilted it used curves, feathers, pretty much anything you can imagine so when you look at the back of the quilt, you really can't tell that it was a log cabin on the front.
Only thing about log cabins is the number of seams. If you did a postage stamp quilt (2 " or smaller squares), you wouldn't necessarily do SID. So don't worry about it.
I suggest you pick a continuous line pattern you like and just do it. Good luck!
P.S. I just finished my first log cabin and used meandering, rose flowers, rope type circles and all kinds of other designs. It turned out great.