Please see stoichiometry of compound that should be prepared, typically the most common stoichiometry is CuAl2O4, a spinel. For this stoichiometry is necessary to "mix" 0.5 mole of Cu2O and 1 mole of Al2O3, for this ratio Cu/Al it is possible some kind of mechanical processing.
In the absence of further structure based on the mechanical or high energy ball milling, you might use another mechanical way type food mixer and a proper fluid to disperse each powder and both powder.
Correct and is use a very volatile fluid (never H2O) type isopropyl alcohol, cetone... Here, a protocol should be developed. Careful with bubbles trapped. After, mixing this kind of barbotine should be poured at recipient with very great surface area forming a thin layer of barbotine. This feature provides further condition to fast vaporizing of solvent avoiding separation of oxides. Typically, a glove box with forced air atmosphere with temperature above of vapor one of solvent is used. After dried, the powder mixture should be "deagglomerated" in agate mortar sufficient to way by a sieve 350 mesh.
First of all you must consider the stoichiometry of the desired compound. The selected ratios of Cu2O and Al2O3 powders must be mixed very well in an agate morter. Then the mixture is placed in the electric mill which equipped with stainless steel spheres. The grinding process must continue for long periods (more than 36 hours) to insure the formation of a Solid state reaction.
For more details, you can refer to my ٌResearchGate page to reference some systems were prepared by this mechanical technique.
combinations of magnetic stirring and ultrasonication can do the job. fisrtly, dissolve the stoichiometric amount of powder into an appropriate solvent (water, ethanol, methanol etc.). Then use magnetic stirring and stir for about 20minutes. Thereafter sonicate for sometimes (1hr, 2hrs, 3hrs etc.) . dry the slurry in an oven for about 12-24hrs. crush the soft agglomerates using mortar and pestle. Finally get your powder.
As you start with solid oxides, ball-milling or mixing in agate morter is only possible ways...
Some off-topic idea...
Are you interested in making mixed oxide phase .. if so ... there are simple chemical methods (e.g. solution combustion method: http://www.sciencedirect.com/science/article/pii/S0925838810017585) which start with basically solution of nitrates of Cu/Al and results in homogeneous phase ; without any milling or mixing.... As this method start with solutions the intimate mixing is easier...
You should explain, why you want to avoid the ball milling process.
Is it because of possible impurities or are there any other reasons?
You can always just mix the powders by "hand". It would just need to be done for a much longer time.
You can also use solvents to better "disperse" your original powders and that would then help you getting a better mixed system. Afterwards the solvent is being removed under vacuum or slow heating. Just make sure you slightly continue to mix your material during the solvent removal.