Would it be possible that a dentist remove a wisdom tooth or is it better to have an oral dentist?

Remove wisdom teeth: Not quite sure what the difference between a dentist and an oral dentist is unless you mean oral surgeon. That would depend on the condition and location of those wisdom teeth. Some general dentists enjoy the surgical treatment and are quite good at it. If there is any chance of complication i personally would see the oral surgeon who is usually (not always) better equipped to handle them.

Sure: They can do quite a bit sometimes, hence the name "general dentist". But with root canal therapies i would want someone who does this each and every day all the time - an endodontist. For braces- an orthodontist. For gum work - a periodontist. For wisdom tooth extractions - an oral and maxillofacial surgeon. With an oral surgeon you also have the added benefit of sedation available.

It depends: It depends on the tooth's position, the tooth's root structure, the dentist's skill and confort level, and your desires. Some wisdom are very easy to remove and require no special effort; some are exceptionally difficult and require significant surgery. If you trust your dentist, follow his recommendation. If you would be more comfortable having a specialist remove it, see an oral surgeon.