Show animation without Animate frame and controls

Maybe this will get you started. The idea is borrowed from my answer to How to add the pause button to that dynamic stopwatch? It uses Clock instead of Animator.

cAnim[x_] := Graphics3D[Rotate[Cuboid[], x Degree, {0, 0, 1}]]
sqAnim[x_] := Graphics[Rotate[Rectangle[], x Degree]];
anim = cAnim;
offset = Clock[{0, Infinity}];
{Button["CUBE", anim = cAnim; offset = Clock[{0, Infinity}]],
 Button["SQUARE", anim = sqAnim; offset = Clock[{0, Infinity}]]}
DynamicModule[{time = Clock[{0, Infinity}], stop, dt = 3},
 Dynamic[
  If[(time - offset) 90/dt < 90,
   Refresh[
    time = Clock[{0, Infinity}];
    anim[Clip[(time - offset) 90/dt, {0, 90}]]],
   anim[90]
   ]
  ]]