a small amount of frame springing isn't usually a big deal but I've seen enough sprung frames break to know that it almost certainly increases the chances of breakage. So if you are going to fit a wider wheel, its best if you know it is a permanent change and you cold set the frame to match it.
If you are going to cold set it I too favour some method whereby you do one side at a time (as per Colin or Mick); most frames don't 'give' each side evenly, not least because there is often a big dink in the RH chainstay. Note that even a small dropout misalignment can hasten the failure of the axle or the dropout itself, so check this carefully and reset accordingly.
Note also that if the frameset is CrMo and
it has been brazed in a bit of a rush the chainstays could be lacking in ductility. On any older frame there is a chance of corrosion inside the frame too. Thus cold setting an older frame in unknown tubing is never entirely risk-free.
BTW although I've cold set many frames wider (and at one time would have done this to your frame without a second thought) I have since begun to question this practice; not because 'it doesn't work' per se (it usually does) but more because the several of the reasons for cold-setting such framesets are now less relevant, for example;
- 'to give the machine more gears' ; well you can get the range
some other way, and unless you are riding flat out in a group, larger gaps between the gears are not as important as most people suppose.
- 'to allow the use of contemporary parts'; -well I don't think it matters much between 5s 6s or 7s, there's not that much choice in decent quality new stuff...
On the other hand there are good reasons for leaving it alone, eg that if you are riding a frameset from the 50s or 60s and you can do, you may as well build it up with period correct components where possible; in another ten or twenty years time the use of such machines (when they were new) may well have fallen out of living memory and such a machine will be seen more as an antique.
If you want to have your vintage cake and eat it, there are a few options for 'more gears' on a non-period correct rear wheel around 120mm. Obviously this doesn't stop you from using a period correct 120mm rear wheel when the fancy takes you.
- a compact 6s freewheel. These were quite common at one time; Maillard, Atom, Sun Tour etc all made them and you can still find them on e-bay, at cycle jumbles etc. You can sometimes make your own by taking a 7s freewheel and (if the top two sprockets are threaded and overhang a short body) you can simply delete the smallest. If this means (say) losing a 13T sprocket, I'd argue that you are not missing that much if you don't have it.
- freehub options. The very first shimano freehubs were available in 120mm 5s versions. If you can get a hub like that, you can (by modifying one spline on the sprockets) fit sprockets from any modern cassette onto the freehub body (except in the top position which uses a threaded sprocket to retain the others). Using this approach you can build (say) a 7-from-10 cassette hub that is about 120mm width.
In point of fact for the latter approach, all you need is the 5s freehub body itself; although not originally bolt-secured, it turns out that these 5s freehub bodies can usually be secured to later shimano hubshells using the bolt-securing approach. The bore dimensions and drive spline interface are common between early bolt-secured freehub bodies and the previous non-bolt secured freehubs.
- Because there are many people wanting to preserve the originality of older frames and yet gain the advantage of modern technology, you can now buy cassette hubs in narrower OLNs for older frames. eg compass bicycleshttps://www.compasscycle.com/shop/components/hubs/grand-bois-120mm-cassette-hub/