No you can’t get bits data through the API without an app, currently the only bits related endpoint is the Bits Leaderboard https://dev.twitch.tv/docs/api/reference/#get-bits-leaderboard and that requires the bits:read scope, meaning you need to create an app and have the broadcaster go through your OAuth process to grant you a token to access that endpoint for their channel. All future endpoints relating to bits will also likely require that scope too.
If you want to create a record of cheers as they happen you can either connect to Pubsub https://dev.twitch.tv/docs/pubsub/ and listen to the relevant topic (again requiring an OAuth token, so you can’t do it without creating an app) or by listening to the Cheer events through Twitch Chat. Either way that only gets you events after you start listening, there’s no way through the API to get historic Cheer data.
Also as a side note, Cheers are not donations. Donations have specific legal meaning that effects tax law and stuff which means it’s an important distinction that Cheering bits to a channel is not a donation to them.