Replacing ugly tinny fin-tube convectors with thin profile "radiant" cast-iron recessed convector/radiators would be both better looking & more comfortable. They're wicked-expensive new, but can often be had on the cheap from antique renovator-supply houses (tried Craiglist?) or others.
Try to figure out the output specs for your dusty-crusty convector, see if you can't find a cast iron convector in a similar range. Once you've gone with cast iron radiant convectors or cast iron radiant baseboard you'll never go back to the cheezy fin-tube stuff (if you can afford it.) They're re-paintable (use a paint rated for your water temp though.) I usually find 36-40section versions at scrap-iron recyclers or Craigslist for a hundred or two 'merican shekels, clean 'em and paint 'em. If it's in the budget, a light sandblasting & bake-on auto paint can be GREAT looking, and still cheaper than new in standard colors (or primer.) They're typically ~5" deep, ~ 20" high, from any vendor. (Burnham Sunrad, Burnham Radiant, etc.)
Low profile Euro-panel radiators with convector channels look sleeker, but are even more expensive. A dressed up repainted Sunrad color-matched to your trim or walls can be pretty fine, if slightly old-school. (And they work great with low temp water too, unlike fin-tube which craps out considerably once you're in the ~ 120F range or lower. In my own home I run them at the same temps as the radiant-floor water.)