You really are conflicted. It would be good to face that full on and deal with it as an issue before you proceed.
Being afraid to handle your chickens is a pretty big stumbling block. As with anything we need to do but are very fearful of it, it's best to address it in small stages.
First of all, messy butts and checking for parasites is not a life threatening situation, so it's possible to take some mitigating steps prior to taking on this operation in order to prepare both you and your chickens for it so it doesn't need to be so stressful.
I suggest you take a few days to condition your chickens to come to you willingly. It's much easier than you think. This lesson will be for the life of your flock and will save you all future stress and major hassle. You can get this sense of dread conquered and left behind.
First step is to figure out what their favorite treat is, one they can't say no to. For most chickens it happens to be scratch grain or cracked corn or live meal worms. If you select a bribe (treat) that is silent, such as live meal worms, it helps to come up with a verbal cue or audible signal such as a clicker to use as you distribute the treat. Shaking the container of grain and even the sight of the container will conditiion them.
Do not try to touch your chickens during the first day of this training. On the second day, they will be much more eager for this game, so hold out the treat instead of tossing it. Make them come in to take it from your hand. Do this slowly in a relaxed manner, and again, don't try to touch them.
On the third day, hold the treat in close to your body so they need to come close to you. If none are showing any fear, go ahead and stroke sides of necks as they accept the treat. Later in the day, repeat the lesson and this time try gently bringing a hen in close to you without picking her up. Cuddle her close as she stands between your knees, and chances are, another hen will choose to muscle in on the action. When this happens, you've got your flock conditioned to come to you whenever you need them to. Reinforce this behavior frequently.
When you think you're ready, choose the most friendly chicken (you will know which are pushovers and which ones may need to be tricked into coming close by this time) and she will be your first "client" for spa treatment. Take your time and reward her with a treat before and after the butt washing and exam.
Take one at a time at your own comfortable pace, working from the most friendly down to the least cooperative. Even the most uncooperative, though, will be pretty easy to sucker in close enough by offering a treat then trapping her with an arm as she accepts it.
Soon, you and your flock will be able to interact without anyone getting stressed by the need to chase and grab.