> Such as?
https://en.wikipedia.org/wiki/List_of_countries_without_arme...
Mostly the European microstates and several Caribbean and Pacific islands, but if you don't count a gendarmerie as armed forces, you could include Costa Rica and Panama--two not-tiny countries--in the list. (If you do count them, the largest is the Solomon Islands).
> And for a further question, would they have remained stable if other countries had not invested in their military to the point that the world in general remained peaceful?
That this question is being asked is I think a concession of the underlying point: fiat currencies aren't maintained by military investment, not in the same way that Bitcon is maintained by hashing power.
Furthermore, it's not at all clear that the decrease in active conflicts over the past century or so is really due to military investment. One can argue that the establishment of international communities such as the EU, or the UN charter forswearing territorial changes via war has had as much, or more, of an impact on reducing the outbreak of wars such as the War of the Pacific as American military might did.