Like others have said, a hand pump is going to be a real pain. If you don’t feel like pulling a vac with your source turbo, a cheap vac pump of Amazon or eBay would work about a million times better than a hand pump. Heck, you can even get a cheap pump from harbor freight that will do the job pulling on a buchner just fine.
Add a little cake of celite on top of your filter paper to step up your filtration game.