Is there a specific name for swear word alternatives? I know about synonyms, but was wondering if there is a specific word to describe when a substitute is created for a swear word (e.g. "dang" or "shoot").
There a a few terms that I might use to describe speaking in this manner. The most likely is minced oath. As the link to Wikipedia describes, this refers to substitution of vulgar terms with approximate terms that are considered less vulgar, including your examples of dang and shoot, and adding fudge, doggonnit, heck, and others. The term itself derives from mince, meaning to make small, and oath, meaning a judicial swearing.
Another term that could describe this is bowdlerizing. This also refers to replacing words that might be offensive to some with a more innocuous version. However, this term usually applies to entire passages or text, not individual words. It still might be what you want, but less likely.
Finally, this substitution can be described simply as censorship. This term tends to have a bit more of a charged meaning in common usage, but it doesn't necessarily have to. A person speaking as you describe might be practicing self-censorship.
is a nice word that entirely replaces a swear word with an existing word that could be used in polite conversation, for example 'feces' is a euphemism of 'shit'.
on the other hand, is a slight change in pronunciation of a taboo word, that weakens the force of the taboo. For example, 'shucks' for 'shit'.