Hi @richard64
I want to mention this first – we are having sporadic Upload issues at UseGalaxy.org, so if that is where you are working, please wait to do this until after this issue is resolved. See → Uploading to usegalaxy.org - #8 by jennaj
I’ll try to address your questions 
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Loading from an external drive through to your computer then up to a website.
Try this with smaller files first as a test. Sometimes people have slower data transfer rates from external drives up to any website, not just Galaxy. You can compare with something like Google Drive. The transfer to Galaxy will be about the same as any other website.
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Data security at public Galaxy servers
Remember that public Galaxy servers are not appropriate for certain classes of data. Protected human clinical data is one example, but it could be processed in certain Galaxy deployments like this one → AnVIL - Galaxy Community Hub.
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Data security for other cloud providers.
Dropbox is one example, and AWS S3 buckets are another. Whether to keep you data in the cloud is beyond the advice I can give here – I can only say that transfers between two cloud environments will always be “faster” than data coming from a laptop’s external drive.
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Upload speeds.
It sounds like you are working from a consumer internet connection. ~ 8 Mbps will be pretty slow to transfer ~ 40 GB of data (12 hours per file!). And that isn’t counting the speed from the external drive, or any throttling your internet provider might apply once they “see” the large transfers. I think you’ll need to find a faster connection to get those large files anywhere else but you could contact them and ask.
Hope this helps! 