Sorry this is not necessarily helpful - I understand you may just want to off-load the records and given the circumstances, whatever you choose to do is absolutely fine.
I have a funny (not good) feeling about (usually) larger charities cashing in on things such as this
I would support my local record shop and offer them first refusal. They are often trading on very tight margins, if maintaining an actual shop front and mainly trading in second hand records. Most at least are very welcoming and will allow patrons to chat, drink coffee and most importantly listen and enjoy much of their stock.
Anything of any rarity/value donated to the larger established charities seldom winds up in their shops (they mostly sell clothing) but instead gets auctioned online via eBay. They tend to no longer stock much in the way of physical formats and what they do stock is often well overpriced1. With Buy-it-now/Best Offer auctions they will often top prices and refuse reasonable offers. Traditionally, charity shops were the only chance that people had of experiencing classic2 music. People used to be able to enjoy music at home that they wouldn't otherwise get to experience. Now instead, the art either ends up in landfill (less well known/accomplished artists) or the preserve of the well off.
I feel music on records and other media is much better enjoyed by enthusiastic people rather than getting left unplayed in a welathy collectors private museum.
1: At least speaking for the charity shops around here, including Oxfam whom are amongst the worst culprits
2: Inclusive of classical music as well as greats from other genres