This is what I recommend:
I don't recommend you buy cat/dog wormer as you can't tell how to dose it without a math degree and it's meant to be given on food.
Buy Wazine 17 (piperazine 17%) which is via water. Give taht one day as labeled. Withhold all eggs and meat for 14 days. Then give the ivermectin that you can give in the water.
On the day of worming and one week afterwards, give yogurt every other day for a week to replace bacteria lost during stress.
The reasoning is this:
One worming with wazine, which only kills roundworms, gets you started by killing most but not all of the roundworms. Since you haven't had a fecal egg count done by a vet, you don't know if your birds are wormy or not. If you kill ALL the roundworms and the bird has a lot, you can make it go into anaphylactic shock or die from clogging. I've had friends who had this happen. So you worm gently and rather ineffectively first - on purpose.
Then you worm the following time and every time thereafter with ivermectin. Ivermectin is very safe for the bird but deadly for worms. It will kill (nearly) everything at once. So you don't want the bird to be fully infested the first time. Thus the wazine starter. The ivermectin will kill everything else (except tapes and protazoa) including mites and lice that take blood.
Then worm with ivermemectin twice a year thereafter.
You can use DE in the bedding in between to help prevent the hosts of worms and help with lice/mite issues.