First of all, to the original poster, sorry to hear of the unexpected loss of your marriage. That is generally traumatic at any age. After 60, it must seem especially hard to imagine “what next.”
In my case, hopefully that will remain forever a hypothetical... but that is unlikely, since DW is significantly older, and has a progressive condition. Have thought sometimes about what one would feel, and do, after losing a long, happy marriage, and being “of a certain age.”
Although there are probably many women with whom one could get along well... it’s hard to imagine anyone having a spirit comparable with DW... and although apparently it works for many, it doesn’t sound at all fulfilling (to me) to have one of the “nice companionable relationships with no intention of marrying.” Those always sound... “nice”... but without the deep felt bond of a true affinity of souls. Not to disparage those arrangements for people who want and enjoy them, but in my case, I think such an arrangement would just underscore the past loss of DW, and what would still be missing. If I wanted a companionable friendship, I think I’d prefer to keep it just a friendship, and nothing more... and although I know I’d prefer to live with a deeply felt bond, I suspect it would be very hard to find after DW.
And in the hypothetical situation after DW... hopefully would be very cautious and discerning about people’s real natures, and real motivations. (As others have said, don’t jump into anything, just to be in a relationship.) The only relationship worth pursuing, in my case, would be with a woman who, like me, would want to discern the real nature of a person, to see whether there are grounds for a deep affinity. If, as an older male, one heard women speaking of men looking for a “nurse with a purse,” as the saying goes... one would tend to keep looking. Caution is good, but when it graduates into cynicism, it obscures the quest to understand the real person. After many years as caregiver for a significantly older DW, I would only consider a relationship with someone who sought to perceive the real person.
And maybe that’s the main thought for the original poster, and anyone in that situation. Life is short. If you look for a relationship, seek to perceive the real person. And make sure that they too are someone whose primary interest is to see the real person who you are.