Abbreviating "of course" to course or 'course - is apostrophe needed to indicate missing word?

The use of an apostrophe to indicate the omission of complete words from a contraction is rare but not unknown (o'clock). Lynne Truss, in 'Eats, Shoots and Leaves', includes 'the attempt to represent regionalisms and the like in print [often accompanied by a forest of apostrophes]' [paraphrasing] in her list of acceptable uses for the apostrophe, but does not include this example. I'd say that the unapostrophised version Course (when used in sentence or fragment-initial position, and followed by a comma, a 'not', or a variant on 'he/'e is') is, as you indicate, hardly likely to prove ambiguous or lead up a garden path.

Here is an example from 'Echoes of a Trumpet - a legend of Selborne after the Riots; Jean Newland; 1998:

James saw this and tried to reassure them, "I'll be alright. It just takes a bit o' gettin' used to, that's all. I won't let yer down, I promise."

His mother smiled, "We know yer won't, son. Come on, off to yer bed. Y' need yer sleep. Meanwhile, I've got to find yer somethin' to wear for tomorrer."

"Could I have a little more broth first, please ma?"

"Course yer can, son. 'Ere, I'll get it."

And another from Glenice, Crossland in 'Christmas Past' {2007}:

"Can I? Be in your gang? Are you sure?"

"Course yer can. We could do with a good mechanic to look after us bikes."

I'd avoid opting for the apostrophe, but it's really a style choice rather than observance of a well-defined rule. And representations of dialect are not going to be correct as regards standard usages, so worrying too much about this point would be precious. And in fact, the transcription of 'Brassed off' here includes an example using the apostrophe (the transcription does not include inverted commas):

Nurse: Is this man bothering you?

Phil: 'Course he is. He's me dad.