(Disclaimer: by no means a microwave expert, though I've dabbled...)
Yeah, a classic IF mixer/downconverter would be a typical choice (e.g. the venerable MC13154, although it's only good to 1.8GHz). At those sorts of frequencies, something like a RFFC5072 (just found from a quick search) would get you in the ballpark of your DSA815's 1.5GHz, or you could do a double conversion.
Would it be good enough for dicking around and looking at stuff? Sure.
Would it be good enough for side-by-side relative comparisons/measurements? Probably.
Would it be good enough for absolute or long-term measurements? Hmmm, not without some serious thinking applied to the design.