NO. Please get yourself a properly honed straight razor.

My experience with shavette's is that they are more grabby as I have a feeling they may be a bit sharper, but not "finished" properly. I mean that the edge more than likely has more micro-teeth than a properly honed straight (I have not observed the edge of a shavette under magnification) . I have yet to get a smooth shave from a Shavette, but my straight shaves are stellar.

Your first few shaves should be with the grain (wtg), you are on the right track there. Keep at it and you will be more than pleased. If I can be of assistance, please don't hesitate to contact me.
Scott