Measuring the specific electrical resistance would be very difficult and very subject to erroneous measurements. It only works with wires if you want to perform such a testing.
Unfortunately, titanium has no measurable magnetical properties so checking with a magnet would not work.
The best way to analyze metal objects like these is by atomic absorption spectroscopy but I presume you don’t have the apparatus and you have to take a monster of the case. However, if you can send me a monster (very small would be sufficient, about the size of a splinter), I can make such an analysis for you if you want.
The easiest way to determine the case material (if no alloy!) is indeed a density check. But you should measure the total case volume and not the volume of case + empty indise volume like mentioned above, if I read well. Fill a glass vase with water and a drop of detergent (to decrease the surface tension of the water). Mark the top of the water column on the vase and sink the case in the vase. Now mark the top of the column again and measure the distance between the lines. It’s an easy way to calculate the volume of the rigid case material. Now divide the mass of the case by the volume and you have the density. Compare that with the known densities of aluminium and titanium.
An alloy might be possible as well of course. Then any “household-method” measurement would be useless because the exact ratio of the alloy components must be determined first.
Feel free to contact me if the household method doesn’t work!