Dye it or don't, the choice is yours. If you dye it, let the leather absorb the first coat for at least 20 minutes then rub it down thoroughly with a bit of flannolette to remove any excess. Give it a second coat if required and repeat the rub down with a fresh bit of cloth. Seal the leather with some leather dressing and let it absorb into the leather and give it another rub down. You really should have no problem with dying the leather and the dye should not harm the razor as you should be ensuring the razor is clean and dry before putting it away.I would also recommend using an alcohol based dye and not a water based one. You don't want moisture trapped in the leather from mis judged drying time prior to sealing. Just my advice on the subject.
Also whatever you use to seal the leather, be it neatsfoot, saddle soap or a dedicated leather sealer will change the draw of the strop in different ways. Experimentation will be the only way to find what suits your tastes best.


Mick