Do the following sentences mean the same thing?
Just so let you know that our uncle is not in good shape.

Our uncle has a disease.
Would you say that he's not in good shape or in good health.

Question

Do the following sentences mean the same thing?
Just so let you know that our uncle is not in good shape.

Our uncle has a disease.
Would you say that he's not in good shape or in good health.

Answer

'Good health' is the well-being and absence of disease. 
'Good shape' is a state of fitness and good health as well 

So in case of your example you can use both  , yet if you want to be specific ,it is better to use 'good health' since it is related to disease.The presence of disease means not being in good health in particular.

Answer

Just TO let you know that our uncle is not in good shape.

The phrase is perfect. 
in good shape = 好好儿
This is NOT the same as having a disease.