It might be worth doing something to the inside, if the instrument is in fact worth keeping. For almost all wooden whistles and recorders I own, I have re-oiled the bore at the same time as cleaning the windway properly. This requires getting the block out. The process sounds scary but I haven't had it go wrong yet, and I've done it to recorders and whistles of considerable value and rarity. (Any repair person will do exactly the the same).

You need

- a length of wooden dowel (or plastic rod, I prefer that) a bit longer than the inner length of the headjoint (or complete whistle, for one-piece instrument), and slightly less than the internal diameter of the headjoint, with a flat end;

- a firm hard surface, like a concrete floor or butcher's block;

- a sock.

Put the sock over the top end of the headjoint. Insert the dowel into the headjoint till it contacts the block, evenly. Then lift the headjoint and dowel and BANG them down on the hard surface, with a force comparable to hammering in a nail.

The block will fly out, and the sock will stop it hurtling across the room and finishing up under some piece of furniture you haven't moved in years.

You will now be able to see and remove all the dirt that's built up in the headjoint since the instrument left the factory. (Usually this will not have been done before). It is also much easier to oil the headjoint if you can pass a swab right through it. (I prefer not to use a swab - after cleaning the bore out, I use a smooth dowel coated with oil, and roll it around inside the bore until I can see I've applied a smooth oil coat over the entire inner surface).

I have used almond oil, but it goes rancid easily. I now prefer peanut oil. DO NOT use a drying oil in the bore.

You then push the block back (you don't oil that) into the correct alignment, so the bit that contacts your lip forms a smooth surface. You will need to get it into place with a series of very gentle but sharp taps - if you go too far you can always whack it out again with the dowel. Leave it a couple of days before trying it so the oil can soak in. You should hear an obvious improvement in the clarity of the sound.

I'd just leave the outside, except that for a tenor you might want to take the key(s) off (precision pliers if the shaft isn't threaded) and re-lubricate it(them) - the suspended-particle Teflon or graphite lubricants used for performance bicycles work best; lubricating oil tends to go sticky.

Plastic instruments usually have the block glued in, you can't knock it out.