It's hard to answer this question without knowing what the delicate parts are, and what type of circuit card assembly (CCA) it is and its intended service environment, and the flux chemistry being used (RMA, no-clean, or water-soluble).
There are spray pressure devices you could probably purchase that would give you the spray pressure reading as opposed to the supply pressure reading (gauges that display water pressure in PSI) that nearly all in-line cleaners have. But even if you could theoretically mount the pressure reader on a fixture, run it through the wash, and "profile" the wash so to speak, how would you know what pressure is going to be needed to not damage the components?
The damage can also be due to variations in the water temperature for a given pressure. Partially clogged spray valves can give you variations in spray pressure also.
I think the best way to determine this may be to get some scrap parts and solder them to some test boards. Are solder coupons or scrap PWBs available from the board fabricator?
Keeping the water temperature at a given setting, you can vary the water pressure readings in the supply lines to the spray nozzles to determine what is the safest combination to use. Realize you will need to check all of the sprays, as most in-line cleaners have an initial spray, secondary spray, and final rinse spray.
You may also want to document the air knife pressure also. Run the test boards at incrementally higher spray and air knife pressures and inspect for damage to the scrap or dummy components after each pass. Keep in mind that the pumps may need a minimal spray/flow rate to operate safely. Check the manual for the in-line cleaner you have, and talk to the machine supplier.
They may also have some good advice regarding the spray force and volume requirements. Wash baskets with the right screen size inside of them may be enough to deflect the direct spray and protect the parts. For example, a wash basket with the right size screen above and below the sensitive parts, but not necessarily over the whole CCA.
Another option is to not run the assembly through the in-line cleaner, but have an ESD-safe wash tub and adjustable spray wand set up using the de-ionized water in your supply, with a drain filter feeding the water back into the de-ionized water loop. This requires manual intervention, however, and having an operator cleaning the boards in the tub may add handling and labor cost issues.
There are also batch-style "dishwashers" and solvent vapor degreasers that are gentler and can be loaded, set, and run without any further operator involvement. This allows you to not have to adjust the spray pressure on the in-line machine, where a higher pressure may be required for cleaning other more robust products.
Again, the type of batch cleaner to be selected and the solvent choice depends on the flux chemistry being used. Realize that you may be able to use a different flux chemistry for this particular product that better suits the optimal cleaning process.
No matter which safe cleaning option you come up with, be sure it gets the CCA clean. Run cleanliness tests such as Omegameter or Ionograph and monitor the results over time.
If you do not have that option, you should at least send out some test boards to an outside contractor who can test for cleanliness. The level of cleanliness required is dependent on the type of product (Class 1, 2, or 3) and your customer requirements. Qualify the process carefully before using it in production, then monitor the production CCAs. Good luck.