Go for it. Nice white wheel will give much better results than the side of an ordinary grey wheel. Especially compared with the standard budget wheel found on most affordable grinders which are, for obvious reasons, made more to be safe when mishandled by the inexperienced DIY folk than to give wonderful results for the more experienced.
A narrow white cup wheel worked fine on my old (cheap) Whitcote double ended grinder for drill and tool sharpening duties for many years until I got my Clarkson T&C grinder.
I added a spindle extension to the Clarkson to take one of these relatively inexpensive Axminster wide white wheels **LINK** for drill grinding duties. I'm well pleased with the results. Unfortunately out of stock for the next couple of weeks.
I bought an inexpensive wide table to fit alongside the wheel face to handle lathe tools and provide a rest for the diamond dresser. Made it quick detachable so pulling the Picador sharpener out of its mount provided space for the table. Table angle adjustable in the usual way. Unfortunately the one I got is no longer sold and current versions are (unnecessarily for this job) improved with commensurate price tags.
I'd seriously consider hollow grinding your lathe tools on the periphery of your existing grey wheel, using appropriate spacers to set the tool height correct for the right angle, with a final touch up on the white wheel for a really nice edge. Probably get around five touch ups before reshaping the hollow grind.
Clive