Help! How can this screw be removed?

Aarumph! I always thought that the base of the flag pole wasn't properly attached to the wooden band on top of the FB in my boat.
And now that I finally decided to remove it and find another solution, I realised that I waited a bit too much, 'cause one of the screws has already given up - for metal fatigue, I suppose.
Anyway. can anyone suggest a way to remove the broken screw, without making a huge hole and hence reducing the strength of the wooden band?
Which is iroko, just in case it can make any difference. Thanks in advance!
Screws.jpg

from your original post it would appear that you want to remove the fixing rather than refit it, as such, I would suggest you need to find a plug to match the original wood grain etc or leave it in there and sand it down.
 
Tube

rather than using a hole cutter I would use a small plug cutter around it then mole grips but a better way is to find some small steel tubing with an internal dia' a tiny bit bigger than the screw shaft dia' .Hacksaw a number of teeth on the end then use it as a drill around the screw Provided its strong enough and you keep cleaning the waste away and have a glass of water there to keep cooling the tube you should be able to run down over the screw till it comes out then glue and plug with a small dowel.

I have collected several pieces of thick walled tubing over the years for that purpose.
 
rather than using a hole cutter I would use a small plug cutter around it then mole grips but a better way is to find some small steel tubing with an internal dia' a tiny bit bigger than the screw shaft dia' .Hacksaw a number of teeth on the end then use it as a drill around the screw Provided its strong enough and you keep cleaning the waste away and have a glass of water there to keep cooling the tube you should be able to run down over the screw till it comes out then glue and plug with a small dowel.

I have collected several pieces of thick walled tubing over the years for that purpose.

Couldn't agree more.
There is no way you will drill out a s/s screw of this size or use a stud extracter as suggested in other posts.
Do as Fergie says and use a tube. A good tip for this is to use the shaft of an old golf club which are usually tapered in steps. The steel is excellent too so cut out a length of whatever diameter suits and sharpen the ends as Fergie describes.
The dowel plug you glue in then can be drilled to accept a new screw. :)
 
Wow, thanks for all the suggestions.
For the records, it has been pretty hard also to remove the other 2 screws.
I guess they were originally fit when the boat was built 15 years ago, possibly with a sealant of some sort.
Therefore I also tend to think that the tube is the only chance to remove it.
Otoh, I'm also considering to leave it where it is...
Wadduthink, would I be looking for troubles in the long run, in this case?
 
If you can get any a short length of 1/4" steel pipe will be your friend here. A gas fitter's shop may have an offcut for nuppence with a good enough sob story.

A remaining possibility, but not for the fainthearted, would be to chaindrill around the screw stub with the smallest drill you dare use as it will minimise the size of hole you must plug afterwards. A 1mm drill is a good start and you need to ensure you get to just below the tip of the screw. If you have a Dremel or similar, and some suitable burrs or dental bits, that will run round the screw stub easily.
 
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