Drawing multiple objects using shaders

I have a simple animation with a box and a ball. It works fine but I would like to be sure I am drawing multiple objects the right way and not being stupid/inefficient:

I create and bind VAOs for ball and box, resp. Then in the application program I have code like

   glUniform1ui(objectLoc, BALL); // Send object name to shader.

to draw the ball and similar for the box.

Relevant parts of the vertex shader are

uniform uint object;

void main(void)
   if (object == BALL) ...;

   if (object == BOX) ...;

and there’s a similar switch based on object in the fragment shader for color.

That’s pretty much what I do and with more objects I would add more if-switches.

Am I doing this properly or is there some other cool/efficient way to do things (maybe separate shaders for each object)?

Thanks in advance.