If you were to restructure your design just slightly so that loading the file from disk and uploading the file to the client were not done in the same thread, you could wait for the file to stop being accessed simply by locking out new threads from reading this file, then iterating over all of the threads reading from that file and do a join() on each one, one at a time. As long as the file-reading threads terminate directly after loading the file, the iteration will finish the moment the last thread is no longer reading the file and you are good to go.
The following paragraph is based on the assumption that you keep re-reading the file data over multiple times, even if the reading threads are both reading during the same general time frame, since that's what it sounds like you're doing.
Doing it this way, separating file-reading into separate threads, would also allow you to have a single thread loading a specific file and to have multiple client-uploads getting the data from the single reading pass over the file. There are several optimizations you could implement with this, depending on what type of project this is for. If you do, make sure you don't keep too much file data in memory, or the obvious will happen. But if you are guaranteed by the nature of your project that there will be few and/or small files that will not take up too much memory, this is a great side effect of separating file-loading into a separate thread.
If you go this route of using join(), you could use the join(milliseconds) variant if you want the deletion thread to be able to wait a certain period then demand the other threads stop (for huge files and/or times when many files are being accessed so HD is going slow), if they haven't already. Just get a timestamp of (now + theDurationYouWantToWait) and join(impatientTimestamp-currentTimestamp), and send an interrupt to all file-loading threads in the middle of the loop on if(currentTimestamp >= impatientTimestamp) - then have the file-loading threads check for it in the loop where they're reading file data, then re-join() the thread that the join(milliseconds) aborted from and continue the join()ing iteration you were doing.