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From memory warfarin has an antidote and therefore reversible ( of sorts) but requires monitoring and therefore it intrudes more in your life IMHO.
Other newer anti coagulation therapies are ( AFAIK) not so easily reversed so a trauma or bleed can be bad news but they don’t require much monitoring after you’ve been taking for a while ,swimming sounds pretty safe to me .. I swam a lot during my anticoagulant therapy , I also rode my bike ( not as fast or as long as I used to though )and walked but your GP or cardiologist may say different and that’s THE advice I’d take …. But be honest about ‘a bike ride’, to most,it’s around the park or down the shops not necessarily an 5 hr zone 3 fest or a Zwift race .Swimming , is it an hour in the local pool or 4km in the open water…?
Blood thinning medication has not been recommended for me and I think that consideration of ablation is some way off.
(Also "sport with Warfarin or OACs are pretty risky" sounds very broad - would swimming, for example, present as pretty risky?)