1 The secret of making a radio look good is what exactly you do to its cabinet. Don't forget that many wooden cased radios are 50 plus years old and one expects to see evidence of that when one looks at the cabinet. If the case is in poor condition, then as a general rule, it should be refurbished but I reckon that the age and the degree of tattiness go hand in hand ie. one can tolerate a very tatty 1923 radio but not a very tatty 1955 set. Beyond 1934 or thereabouts do little. Restrict work to light renovating with a toothbrush and warm water. Post war sets consider stripping to bare wood with Nitromors and starting afresh if the top has really bad flower vase rings, damage from the sun or lumps of the shiny finish missing. If you're worried about woodworm rub the holes with paraffin or a proprietary concoction and fill them with a wood filler suitably coloured to match the wood. Woodworm are active if there's little heaps of fine wood dust under the holes.
2 Unless you have loads of time proper french polishing is not on. A good alternative is rubbing down with emery cloth wetted with linseed oil. Apply a wood stain to get the required depth of colour. Do not use modern proprietary wood finishes as these won't look right. They weren't invented when the radio was born. French polish kits come in two bottles. One's the stain the other the grain filler. Application of the contents of these two bottles will give you a good basis but the final treatment with meths is something I've never tried. This gives the highly polished mirrorlike french polish finish you get on a lot of expensive sets of the 50s and 60s.
3 Most blemishes, scratches and the like can be dealt with easily and you'll never know they were there. I use a bottle of scratch remover that was sold for doing violins. Water marks are sometimes tricky. These are white marks on a wood finish and can be removed in one of two ways. Sometimes an application of paraffin will get rid of a water mark but I've found the best method is to hold a lighted match close to the area and the mark will simply fade away.
4 Sometimes a cabinet will have two different shades or a black decoration against the wood. Often the wood is the same but it's stained differently. Black is often a paint finish. If it's tatty the latter will usually respond to the application of a black felt marker pen. Two shades of wood can be achieved by selectively staining to a darker degree.
5 Veneers are often used on pre-war radios. These can be chipped and pieces may be missing. Cut away the damaged area to a linear form and a new piece of veneer can be stuck on. Try and match the grain and after staining the repair won't be obvious.
6 A word about dials. These are absolutely paramount in importance. NEVER try to clean a dial without the greatest care being taken. Never use a solvent cleaner. Use a moistened cotton bud and try to avoid any of the lettering. Use the lightest touch and the dial can be restored to a clean condition. It's possible to signwrite damaged areas but these repairs rarely look good. Always clean the reflector plate behind the dial and any clear glass fronts and fit nice new bulbs as old ones often get silvered inside and are pretty dim.
7 If a speaker cloth is very faded consider removing it and turning it over unless there's a pronounced shadow from woodwork fret. I successfully dyed an old cloth that had faded from green to light brown. I could tell because the bits under the wood surround were still the original colour.