Beading a pet collar

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Is it safe to bead a pet's collar? Tonight at Walmart I bought a small cat collar for my little baby Bonnie, a Boston Terrier (she's REALLY little) with the intention to bead it and make her a stylish little collar and maybe make my other dogs Charlie and Dash jealous, heh. What would be the best way to do this, if it's possible? I have "invisible thread" and E beads, but is this a good size? Maybe seed beads would be better? Should I go in rows and pass through the nylon each time, or go up and down and do the beads in a sequin fashion?

Help, please!