Pretty much yes, that's what I'd do if it was me doing it (but I'm no tiler, so who knows how they do it)...I'd use a Stanley knife and a sharp paint scrapper to remove all the old stuff. Make sure the area is dry before you reseal it. Before touching the new silicone you apply, spray it with soapy water to stop the excess sticking where you don't want it, and then use the end of a paddle pop stick to smooth it / clean it up.