Is it possible to slim sleeves without making armhole smaller?

Any competent seamstress should be able to do that without dismantling the sleeve. It's called a "tapered dart," shown below on a shirt back, but can easily be done on a sleeve too.

I think you can slim sleeves without changing the armhole. I think a good seamstress can do this by cutting the sleeve open, closing/decreasing the circumference of the armhole, then creating a new seam. You need to tell the person how much smaller you want the new armhole.

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The fit of the sleeve affects the fit of the whole shirt. Altering the sleeves seems like it should be easy, but in reality you could make the shirt unwearable. Sleeves must allow free movement of the arms and a too small sleeve will restrict movement. Looser sleeves allow for more movement. 

There are three types of sleeves. The raglan is seldom used on dress shirts so that's the last I'll mention them. The set in sleeve has the body and sleeve sewn as separate units then the sleeve is sewn to the body.  If the sleeve is a set in sleeve then it can be altered from the bicep downward and the armhole will be untouched. If the entire sleeve needs to be removed, altered and re-sewn then it can get a bit expensive. It's possible to make a set in sleeve too tight to move your arm.

 The last sleeve style is where the sleeve is sewn to the armhole before the side and underarm seam is sewn. It's easier to add the dress shirt sleeve placket when the sleeve is flat. This one can be altered anywhere on the side seam from hip to sleeve cuff and narrowing the armhole will not impact the body fit the way it will with a set in sleeve. The armhole can be made a bit smaller without as much impact on the overall fit. A standard men's shoulder yoke dress shirt should have one long aide seam from cuff to lower hem. Narrowing the fit of the arm above the cuff is easy, as is altering the side seam. The dress shirt does need some fullness in the sleeve to allow free movement of the arms. A too tight sleeve restricts movement. I could pin as much as  an inch or two away from the seam at the elbow and taper the width to nothing at the armhole and cuff. It would reduce some fullness but still allow movement. I personally prefer to alter right down to the chest line as this fits better. Don't use the word "slim down" that is used for side seams. If you said slim down the fit to me I would immediately think side seams.  Use the word narrow and be specific about the location.  At the place put the shirt on and show where you want the alteration. Pinch the excess fabric exactly where it's too large. The person should pin-fit the alteration on the shirt while you wear it. If it's comfortable then it can be re-sewn. If it isn't then try pin fitting again. Ask for to price beforehand. Get a price in writing so you don't have unpleasant surprises.  And remember, the person doing the work isn't a wizard or magician. Be realistic in your expectations. There are somethings that aren't possible even for an experienced and skilled tailor.