A head catch of some sort is a NECESSITY.... a squeeze chute is not... We do not have a squeeze chute, at any of the places we work cattle. Yes, it would be nice, NO it is NOT essential.
A head catch, stanchion, or something that will catch their head and prevent them from getting their head around to hurt you is necessary. A chute, alley or something that is tight enough to keep them contained is necessary. You want something that will keep them from swinging side to side, fairly tight so they cannot turn around or move side to side. You can use a couple of gates with solid posts to attach them to... to keep them "inline". It needs to be as long as the cattle, even longer by a couple feet. What is known as a "palpation cage" for someone to be able to stand behind an animal... and to be able to not have an animal come up on them from behind... it's a "safe zone" for a vet to work behind an animal or to breed AI or something like that.