How do I dynamically change Manipulate controls?

Question

What I'd like to be able to do is dynamically change the axis of a 3D plot inside a manipulate.

For example if I have a function that has three input variables I'd like a 3D plot using 2 of the input variables and be able to manipulate the third. The part that I've had trouble with is making the axis of the plots dynamic.

This is how far I've got:

axes = {{x, 0, 10}, {y, 0, 10}, {z, 0, 10}};
Manipulate[
Plot3D[fun1[x, y, z], {x, 0, 10}, {y, 0, 10}], {z, 0, 
10}, {{axis1, x, "Axis 1"}, axes[[All, 1]], 
PopupMenu}, {{axis2, y, "Axis 2"}, axes[[All, 1]], PopupMenu}]

which gives me

Any help would be greatly appreciated.

To be more clear;

The axes I would like to change are the x and y axis on the 3d plot. What I'd like to be able to do is select axis 1 = x and axis 2 = z and have the manipulate change to y.

Answer 1

fun1[x_, y_, z_] := (x - 1) (y - 2) (z - 3);
h[u_, n_] := Complement[{x, y, z}, {u}][[n]]

Manipulate[
 Plot3D[fun1[x, y, z] /. m -> m1 /. h[m, 1] -> x /. h[m, 2] -> y, {x, 0, 10}, {y, 0, 10}, 
        Evaluated -> True, AxesLabel -> {Style[h[m, 1], Large, Bold, Red], 
                                         Style[h[m, 2], Large, Bold, Red]}],
 Row[{Control[{{m, z, "Manip"}, {x, y, z}, PopupMenu}],
      Control[{{m1, 0,}, 0, 10}]}]]

Edit

Perhaps this is safer

fun1[x_, y_, z_] := (x - 1) (y - 2) (z - 3);
h[a_, n_] := Complement[{u, v, w}, Position[{x, y, z}, a][[1]]][[n]]

Manipulate[
 Plot3D[fun1[x, y, z] /. m -> m1 /. {x -> u, y -> v, z -> w} /. h[m, 1] -> x /. h[m, 2] ->y, 
       {x, 0, 10}, {y, 0, 10}, Evaluated -> True, 
  AxesLabel -> {Style[h[m, 1], Large, Bold, Red], Style[h[m, 2], Large, Bold, Red]}], 
 Row[{Control[{{m, z, "Manip"}, {x, y, z}, PopupMenu}], 
     Control[{{m1, 0,}, 0, 10}]}]]