The reason you are being hired is that the farmer (or anyone that hires you for that matter) doesn't have the skill set, desire or in many cases the time to deal with the problem so the only way they'd wonder why they hired you to perform services would be from cheap looking equipment and/or low production. Regardless of the reason, if you feel it could be a problem look at how to address it instead of not using the proper tool for the job.
In regard to shooting pigeons, first off, look at your equipment. Would you be using quality gear or would it be something that looks like it came from Walmart's bargain bin? Even when I was using a "cheap" springer (RWS 34 w/ 4x fixed scope) I would always drop in the sales pitch that I use a $600 air rifle, which is what I paid back in 2000, (today, that could be dropped down to $200 for Gamo and Benjamin air guns) which ended most of the "I can do it myself" statements as they won't invest that much money into a tool they only use a couple of times a year at most. These days, I honestly tell them I use a $1,500 - $2,200 shooting system with a $800 night vision system when needed. Again, this stops any "I'll just buy a cheap air rifle and do it myself" comments. Then I do my best to show them what I use. If they still had doubts, those go away quickly as there's no question that I've a bit of dollars tied up with the gear. Lastly, when they see the performance of the equipment at 40, 50, 80 yards and longer they understand why I spent the money I did.
Next, look at what you can realistically expect to do and the time frame it may take. If you're working at a feed lot or milking farm they need the birds gone today and they don't care how you do it. You need to ask yourself if it will be acceptable to have traps that may need up to 4 weeks or longer of prebaiting time to work, how many birds can the trap hold and how many traps and trap sites will be required to adequately control the problem.
Then look at what the bird pressure is (high, medium, low), the time of day the birds are on the property, and if they roost there at night along with how big the roost site is. This more than anything will establish how you need to address the problem. If there aren't a lot of birds during the day, trapping is most likely the best way to go as it won't be financially feasible for you to sit around for several hours if only a couple birds are present during the day unless you're doing it just to get some practice in or test gear. Also, if only a couple of birds are roosting on the property at night, it won't pay to make a night trip. However, if a large number of birds are present during the day and/or night, then you can do an effective shooting program.
In most cases the best solution isn't just one control method but rather a combination of them. When the population warrants it, I recommend doing a shooting program first as it is the fastest method for knocking down the population and then allowing the trapping program to work on the "stragglers". When possible, you can even add other services such as exclusion, auditory/visual harassment, and nest removal to further strengthen your control services.