No, I don't think those would be sufficient. Genetic ancestry is still wobbly tech at best, and there would be the issue when quite a many those are descendants of the enslaved will have slaveowner genetics too for obvious reasons. Records might be usable for some plans I've seen for the US particularly and possibly for the UK for some for of tax credit/refund, but it's not really going to help people in Caribbean countries where that's a large part of the population.
Another issue that even the largest figures out there for reparation, many of which are very unlikely to be sold politically to make it actually happen -- if we divided up whatever large figure you wish by everyone now...yeah, someone may have their rent or mortgage paid for a year, maybe, but how does that solve any of the societal issues that continue on from the transatlantic slave trade, the denial of generational wealth that the recognized descendants of slave owners have been able to build up - it doesn't really create any sort of balance to that, and I think trying to make one equivalent to the other isn't going to work.
Atonement isn't possible, there is no justice to be had here only repairs, and if we're going to do something under the banner of reparation, it needs to produce results (and be able to get enough people to want and be behind to pressure the government to do it because otherwise it won't happen). If it doesn't change anything, it could be viewed as shut up money.
Personally, I think what some Indigenous groups have done could be adapted -- the money put into trust that could grow and an organization makes very low cost, low qualifying loans to people who come forward with a plan (and get support making it) about wanted to start businesses, learn trades, the kind of things that those with generational wealth are able to ask their families for that will benefit themselves and the wider community. The state backed the destruction of families, so the state could back this with the control of the loans in an appropriate committee - in the UK, we could even make it similar to student loans where people who qualify don't pay back until they earn a certain amount.
Internationally, governments and corporations who still take money out of those countries could be pushed with enough social backing to financially support similar projects, like the peer-to-peer lending that is already popular in some communities, but larger.
The thing is, it isn't about whether the government 'wants to or not', it's whether there is wide enough social support to push them to do something. It would need to be huge.
If you want to know who was paid compensation, then you want this database.