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The disposable straight you mentioned sounds like a injector straight much like the Feather or a Dovo Shavette. I use a Feather Artist Club RG and I love it. The blade will effortlessly, yes, NO...

I would fair to say that possibly your prep needs some work or the razor is dull.
As you said, shave once you get out of the shower to help soften the whiskers. And, as you prepare the lather don't...