Amplifiers contain voltages high enough to Kill you even after the amp has been powered Off !!! If you don't have enough electronic experience to identify and discharge the Filter Capacitors which contain these Deadly voltages, take your amp to a Qualified tech. If you don't know a qualified tech in your area, post a request in the alt.guitar.amps newsgroup, the folks there will be happy to help you.
1. Replace the tube rectifier with a "plug in" solid state rectifier. The tube rectifier, (over a solid state one) in a champ doesn't make much of a difference sonically other than reducing your overall volume. This is because a single 6v6 isn't enough to cause any noticeable sag in the 5Y3 rectifier. 1N4007 diodes can be used to build your own SS rectifier which will push the amp to its max capacity, (a little over 6 Watts). But be aware that old or dying caps will Fail under the increase caused by your new SS rectifier. But the standard value caps if they're in good condition will handle it with no problem. (So if they blow, they probably should have been replaced anyway).
2. Replace the 6v6 power tube with a 5881 for a little more headroom. The higher voltage of an SS rectifier also tends to wear out 6v6's much faster. With the 5881 this will never be an issue.
3. Increase the value of the Cathode Bypass Capacitor to 100v. This allows your champ to run "safely" under the increased load of the SS rectifier. Don't change the value of the cap, just the voltage rating.