What alternatives are available to the current tests that candidates are required to undertake?

You could email the candidate with instructions and ask them to undertake a specific test and return this to you e.g. typing, spreadsheets, case study etc. but it would be difficult to determine if this person did genuinely undertake this test or if someone performed it for them.  Alternatively, you could ask more in depth questions at interview about the areas that the test covers or give them an interview question in advance of the interview that requires a more in-depth response.