I do wonder what ATC would expect.
Don’t get me wrong, if I did have to go around from a visual I would be quickly asking to join the circuit (conditions permitting) but surely everything else is going to be lined up with the expectation of an IFR inbound doing an IFR missed approach.
Which IFR missed approach to follow is the next question if you decide on that course of action. Well I would say there has to be a good chance that you will know what approach is in use. 99% of the time it’s going to be the ILS (if available) to that runway. If they have multiple ILS approaches, such as a Z, Y etc then it comes down to either knowing which one they use or are using or being told by ATC. Often the missed approach for these will be the same and it is the IAF > FAF(/P) that is different but not always. Then again, if ATC doesn’t tell you which one you are doing (especially if being vectored for it, where it is almost irrelevant) then you still have the problem of which missed approach (if different) even if you are doing the IAP and not a visual.
But remember you are not established on the approach so how do you get to the missed?
Well I would say most missed approaches will occur on the final approach track, and without thinking about offsets etc there isn’t likely to be much different going around at 1nm from rwxx on a visual and 1dme from an ils.
If you had to go missed at a different point, like on base leg or something or even downwind, then would you not apply the same rules as if you were circling?
There is no missed approach procedure for a visual approach. It is a roll your own type of situation. At some airports in the US, we have a DA or MAP that is further from the runway than the minimum charted visibility required for the approach. In this case, if you meet the minimum visibility requirements, you can continue the approach by flying visually to the runway. The approach charts will have a note: Fly Visual 3.6 NM to runway. If you decide to continue the approach past the DA/MAP, then the missed approach procedure no longer provides terrain clearance using the 200 feet/NM climb. You are on your own if you continue after the DA/MAP.. An example is the RNAV (GPS) X RWY 27 at KHLN.
See: http://www.airnav.com/depart?http://155.178.201.160/d-tpp/1505/00192RX27.PDF
