I work at a single runway aerodrome in class C airspace. The standard missed approach for either runway follows the initial departure track of all the SIDS, due to terrain considerations.
I can tell you that if you are on a visual approach at this aerodrome, and have to go around, and decide to carry out an instrument missed approach, rather than entering the circuit, sooner or later you're likely to get a face full of aeroplane.
If you're on a visual approach, and are unable to enter the circuit from an overshoot, you need to tell ATC. The earlier the better. (Like, when requesting the visual approach.) Waiting till short final is too late.
The appropriate missed approach to perform in this instance would be the MA for the instrument approach broadcast on the ATIS.
The requirements are spelled out in the AIP. (NZ)
If the weather in the circuit area deteriorates during your approach, just make a D and inform ATC asap. Hopefully ATC will have observed the deterioration, and taken it into account.
In a perfect world, the ever-changing matrix we work in would take the regs and procedures into account. Sometimes it doesn't. (Norty weather.) One of the problems inherent in doing every little thing according to some procedure, is that a situation gradually develops that nobody remembers how to use common sense any more.