In general, the ringing you hear is generated from the 'exchange' (mobile network serving the call - ie the network in use for roaming) so will be the national tone/ cadence.
Can think of few easy ways to handle the calls - you could get an 033 (business) number and have it send calls via VoIP (voice over IP) so it could be answered with a suitable internet-connected handset / mobile VOIP App, using the hotel wi-fi, for example (data charges are still high at present, even in Europe, though if you have Three or EE, some countries may work out cheaper).
The firm I use charges around a tenner + calls (+VAT) a month and allows up to 10 numbers (03x, 0800, and geographic - my 0151 number is similar to a taxi firm and I get misdials day and night!). Calls to the number(s) can be automatically recorded and sent in e-mail (not just voicemail, all calls can be recorded), and 'withheld' numbers are not withheld - they get shown on caller display and in the call logging.
Even without answering the calls, it would be possible to use the e-mail tracking of calls (whether or not the person left a message) and simply ring them back, ASAP, explaining you (DH) were on another call or in a meeting.