You could choose to order locally and deliver internationally. Generally, you can just change the web site from their country to yours.
For example, if you wanted to buy this book set. Click on the item, you will have the following URL with loads of rubbish after it:
Change the web site like so:
And it will come up on the US site where you can order as normal.
Note that sometimes, the URL looks like this instead:
This doesn't always work, if it fails, take that number at the end (sometimes a combination of numbers and letters), that is the Amazon product id, you can search for it directly. It is normally consistent across countries. Not everything is available in every region of course.
If, however, you are doing a lot of giving, you may find it easier to register for an Amazon account in that country. That way you can order local to the recipient and save loads on shipping.
You may find though that having a US-based account is useful anyway and shipping rates from there may sometimes be less anyway. You can be a non-US citizen and still have an account with Amazon US - at least you could when I signed up a few years ago.
Other than that, I'm not aware of another tool that lets you do what you want.