I know that the number of 301-redirects can sometimes raise concerns about site speed. However, 1,000 is really not that many. Large e-commerce sites can have 10,000 301s, or even more. Depending on how the 301 files is handled even this large number can be handled in ways that have very little impact on site speed or page load times.
I think the number in your vase is nothing to worry about.
I do think that deleting and 301 redirects is the best way to go for anything that's remotely relevant. For those that aren't, create a custom 404 page and let them 404. Eventually they will drop out of the index. If they don't, you could still file a remove URL request in Google Webmaster Tools.
Hope this helps and good luck!
I frequently vet things here in the forum and it has proven very helpful in convincing other members of my team to go one way or the other. Also, I completely agree with George's suggestion to use the "alt" attribute if it is indeed an image we are talking about, but it appears we are really talking about a bonafide