Hello and thanks for trusting me to help you and your pet today. I am a licensed veterinarian with over 25 years experience and would be happy work with you.
You can use Benedryl, but it is not a very effective medication to cause sedation and even though it may allow a pet to become drowsy, if there is enough stimulation, they can certainly override the effects. The dose is 1-2 mg per pound that your cat weighs so a 10 lb cat would get between 10 to 20 mg. This can be repeated two times per day. The pill that is available over the counter is typically 25 mg. so you may need to go with the children's liquid form which is typically 12.5 mg/teaspoon (or 2.5 mg/cc). Make sure that there are no other "cold-type" medications in it like decongestants.
Another option would be to put him on a towel or even better an opened up pillowcase and pet him until he relaxes and then when he does, quickly scoop him up inside (this is why a pillow case works well) and put the whole bundle in the carrier. This will decrease the likelihood of getting scratched or bitten.
If all else fails, you could consider a house call vet to come to him or have your vet prescribe a more effective sedative that is available by prescription.
Based on your description of his symptoms and his previous spontaneous recovery, I think there is a very good chance that his suspect UTI's are not due to bacterial infections at all and that it could be related to stress. Cats can be affected by a condition called Feline Lower Urinary Tract Disease (FLUTD) which is the name given to a set of symptoms from various causes that can affect a cat's urinary system. The causes are varied and the age of the cat partly influences the likelihood of the cause. (ie older cats are more prone to bacterial infections than younger cats). Other common causes include bladder stones, crystals, tumors, and sometimes just inflammation from an unknown cause (more common in younger cats). This latter condition is called feline idiopathic cystitis (FIC) and is often precipitated by stress and the symptoms often come and go on their own. Unfortunately, they all can show the same symptoms, no matter the cause and all are treated a little differently.
Your very first step should be to have him examined and to have a urinalysis performed which I know you are trying to do.
If it is a bacterial infection, he needs antibiotics. If it is a stone, it needs to be removed. It is possible (and likely) that there are no bacteria at all and it is a problem is due to FIC. The good news is that many of these cats with FIC will improve on their own regardless of what treatment we provide. Usually we try to give them something for their discomfort. It is not uncommon for their symptoms to return again later and can come and go periodically throughout their life. Unfortunately, there is not a test to prove FIC is the cause, and this condition is confirmed when all other causes have been rule out. That is why a urine culture is essential as well as some sort of imaging (xrays or ultrasound) to rule out stones, tumors, etc. (Some types of stones will not show on a plain xray). I would urge you to make sure your vet cultures his urine and doesn't just put him on antibiotics and assume that because he gets better, there was an infection. If he has FIC, it is important to note it as it is often a very recurrent disorder.
In the meantime, I would try to encourage increased water intake as best you can by adding water to his food (as much as he will allow) or providing a pet fountain.
There is a belief that in cases of FIC, stress plays a role. Indoor cats seem to be particularly at risk and there are websites dedicated to helping indoor cats by enriching their environment so as to decrease stress. I am providing one of these links to those websites to you. Regardless of if that is what it turns out to be, decreasing stress and providing adequate mental and physical stimulation can only help.
OSU Indoor Pet Initiative: http://indoorpet.osu.edu/
I hope this is helpful. Please let me know if you have ANY other questions. My goal is to give you 100% satisfaction and if you are not yet satisfied, please reply so I can clarify for you.