Short answer: Personally, my reactions to messing up a word vary from nothing to immediate (but not exclaiming) correction, depending on the kind of word I messed up, how much I messed it up, and the reaction of the audience to me messing up. Big technical words uttered in important meetings get an immediate clarification, at other points I just carry on if I'm sure the context of the conversation is clear enough, or if I see people looking confused I might work the word into a sentence again. Most often though, people will ask before I notice.
If the exclamation is too distracting but you feel you were unclear, make sure to be clear. Following the mispronounced word up immediately is usually done without exclaiming:
...pengrates, sorry, pancakes...
Or move on like your friend does, and if you realize the mistake and see the audience looking confused, repeat the word correctly at a later (but not too far removed) point.
We had pengrates with some awesome strawberry ice cream. I like pancakes, but the ice cream really made the dish!
The first one is easy to remember, and if you do not exclaim (no raised voice, no hurrying up or slowing down) but just act like nothing much happened, people aren't likely to be massively distracted (see also 'long story'). The second takes a bit more practice to remember, and even more to pull off in a natural way, but I found that it often leads to 'relieved' faces of people finally understanding what I meant, and just being able to move on.
No one probably cares much about your stumbling, so don't make a big deal of 'recovering'. Stumbling is something that happens to everyone, often, and while you may notice, there's a very probable chance other people won't. Most research into attention spans and distractions when it comes to processing language are done with test subjects having to remember/recall lists of things, but most of this research seems to suggest that:
A person's verbal memory span tends to be rather short and seems to match the general capacity of working memory:
Verbal memory span, the longest sequence of words a person can repeat in the correct order immediately after hearing them, is strictly limited. In adults, memory span is typically equal to six or seven monosyllabic words. source
If you stumble across a word, it probably results in a non-word, for which memory spans are apparently even shorter:
Immediate memory span and speed of memory search were assessed for words and nonwords of short and long spoken duration. Memory span was substantially greater for words than for nonwords and for short than for long items, though speed of memory search was unaffected by either length or lexicality. source
There is such a thing as an 'irrelevant speech effect', which might be the closest studied thing related to 'stumbling over your words' when it comes to attention spans:
The irrelevant speech effect refers to the degradation of serial recall when speech sounds are presented, even if the list items are presented visually.
When it comes to irrelevant speech effect, you generally either need an 'unexpected deviation' or something meaningful to really distract people:
While an unexpected deviation in the sound (e.g., Hughes et al., 2007) or a particularly
meaningful sound (e.g., one’s own name; Röer et al., 2013) is typically necessary to divert most adults’ attention from a focal task, if general attentional control ability is very low (such as in children of the age studied here), then such ‘extreme’ events are unnecessary for attentional diversion: [...] [source]7
I looked up the article that talks about 'unexpected deviation' and it seems that this talks about a rather significant change, like a single change in voice (from female to male) within an irrelevant speech sequence. So, it seems this falls outside the limits of a single person messing up a single word too, unless you suddenly change pitch and start exclaiming, like one of your friends does.
All of this seems to confirm that stumbling isn't as distracting as you think it may be, and that recovering (by exclaiming) may be more distracting than just moving on and waiting to see if people need clarification/until they ask for clarification.