Vintage Scott receiver repair questions

[Icon_xof]

Howdy all,
I recently obtained an old school Scott R 36 S that needs some work done on it. When it's turned on with speakers hooked up it only hums. The hum is unaffected by input selection or volume control. From what I've gathered this is due to bad ac filter caps (the big cans). I wanted to verify that this is a correct assumption.
When I replace the can caps, does physical size matter outside of mounting issues? I've found replacement caps online with matching farad and voltage values, but they aren't quite the same size.
Also, attached to the leads on the smaller filter cap is what looks like a smaller capacitor. When I found it, I noticed the green casing was split. I flaked off the casing and it looks like the aluminum shell underneath is in tact, so I'm not sure whether to replace it or not. Here's a pic

I also found a row of diodes that have black "stuff" on their leads. I don't know if they were made like this or if it's scorching and they need replaced. Here's a pic:

Well I think that about covers all the questions I have concerning this project. Any input and advice on this is greatly appreciated! And for good measure, here's a pic of the innards from the top:

[ataudio]

Your loud him is most likely your main AC filter caps.  Definitely replace them.  As long as you match values and polarity you are fine.  If needed you can silicone the new ones in place.  The black leads on the diodes could be years of oxidation.  But diodes are cheap, replace them.  The little .22 bypass cap...replace that as well...super cheap.  That looks like a an old tantalum, ceramic,  film cap.....not an electrolytic.  You could even omit it but they are pennies to replace.  That should get you on your way but it might almost uncover other issues. 

[ataudio]

.....should have read DC filter caps....not AC.