I made two pillows like that. Mine were "fake" ultra suede. Which is like saying fake fake suede! Because it was much cheaper fabric than the "real" ultrasuede. We could call this fun with oxymorons, or double and triple redundancies! However, once again, I digress... But... I do think I cut mine on the bias. However, IMO, you really shouldn't need to. The bias is to give the fabric the ability to shape to curves, which doesn't apply to regular pillows, or to give a check, gingham, stripe, etc. a cute diagonal/bias decorative element. All you will be doing here is snipping the fabric flange section of the covered cording one to three times at the corner to allow it to turn the corner, right? I know some take a single snip right at the corner, others snip just about 1/4" to 1/2" from either side of the corner as well. So all of this to say I think you will be fine with straight grain. But I'd do a little sample and stitch it like a corner and just see if you're happy with the results before you commit to cutting straight grain strips. Hope we get to see them when complete!