In the first case, if you enter IMC then you must obey IFRs. Outside controlled airspace that basically means flying an appropriate heading and FL and maintaining IFR obstacle/terrain clearance as appropriate. Upgrading to a radar traffic service would seem a good idea, but is up to you. Non-radio is perfectly legitimate.
Inside controlled airspace means having a flight plan (could be an abbreviated onr over the R/T) and flying as directed by ATC and also having equipment functioning as required for the route and approach as dictated by the ANO.
Some countries don't allow IFR outside of controlled airspace and equipment requirements may vary, so you need to be specific about whose airspace you're interested in.