You mentioned that it happens at some smaller controlled field. Chances are if it is actual IFR (since you NEED to use the ILS) it is probably not going to be super busy. Maybe a few corporate jets coming and going. Don't buy into too much of they "If they are landing one way, that's all there is to it." If you need an approach to get down to mins to get on the ground, do it! They should have an idea with the weather. If tower is reporting OVC003 and one way has an ILS and the other a VOR only only good to 600', they should know that only one of those approaches is going to be useful.

A lot depends on the situation. If I was in a light single shooting an ILS to a nicely sized runway, I probably would take the tail wind up to 10 or 15 knots. I would be hesitant to go much over that. A rule of thumb is what ever the distance that headwind saves you, give up that amount times THREE in tail wind. IE if a 15 knot headwind saves you 400 feet, assume it will take 1200 feet EXTRA to land.

The other thing you might have to worry about is wet runway. If the weather is at mins, you could be dealing with wet or damp runways which may affect your breaking. Couple that with a tail wind you could be looking at really using up a lot of runway distance. Make sure you really hit your touch down zone and not try to make a greaser.

Finally before I step off the CFII soap box, winds will probably be stronger aloft and lighter near the surface. So they may be 10 knots or so at the surface but could be as high as 50 knots at the marker. A light single doing 80 knots needs roughly 400fpm no wind. Add 50 knots, you need almost 700 fpm. If you are not used to that it could be easy to get above and stay above glide path. Then as you get closer you try to correct, over correct (especially when the beam gets narrow, say, at mins) and, well...

tl;dr - tell tower what you need. give yourself plenty of extra landing distance. realize your descent rate will be different and will change throughout the approach.