I have worked before on something similar: cryptomarketplot.com

Free API access is not 1 day but 24/7 on : http://cryptomarketplot.com/api.json ; if you have traffic limits check http://cryptomarketplot.com/api.json.br added a few month ago but not shown on the mainpage (I did that https://news.ycombinator.com/item?id=18653590 )

Only drawback is the limitation to 1 minute resolution. Still good enough if you are not HFT.

If you are HFT they had packages like "all you can eat" feeds. It was like $500/month for the BTCUSD pair on any 5 exchanges out of 75 supported, with different pricing for different latency offers (going all the way to colo!) using custom client and software integration (for SLA on latency targets)

I'd have to ask if they now provide historical data.

If you have precise symbols, date ranges and exchanges you're interested in, get in touch I'll work something out so it's not that taxing on your budget.