The "enterprise grade" approach is modulated sweep, into RF PA, into ISN, into EUT. EUT is grounded (or not) as applicable, ISN is CM, diff, normal mode, whatever you're testing, and other EUT connections are terminated appropriately (more ISNs, CDNs, etc.). Or replace generator chain with transients for applicable tests (usually EFT and surge). This should just fit within your budget, but I will admit setup time and verification/calibration and actually running the test isn't the most expedient process.
A source simply being "dirty", likely won't be a high enough level to be offensive -- 100s of mV perhaps, not 3 or 10V (or as many V/m in the case of radiated tests) -- and will only be dirty at certain offending peaks, not the whole band. If your EUT happens to be relatively immune at those peaks, and vulnerable in the gaps between, well, you haven't learned anything with such a test.
The "dirty" source may also be predominantly CM or DM, or both but in different frequency ranges.
If the EUT is such that, you can make assumptions about bandwidth and linearity -- that is, that it's not particularly likely to have peaks and valleys in its response, and that its response will be roughly proportional to the stimulus -- then a more generic source can be used. I suppose audio amplifiers might be such an example, where the supply noise may be audible in the output even at fairly low levels, and effects like input stage RF rectification aren't very frequency-selective.
Cases where this won't be true, include for example, a lot of things with wide thresholds or common mode ranges (digital logic won't screw up until a volt or two appears across relevant inputs; diff stages won't be screwed up until CM range is violated; etc.), and a lot of things with selective response (radios most obviously, but also synchronous (clocked) digital logic that is only sensitive during a sampling period, etc.).
Tim