While a reverse-proxy approach is not theoretically that complicated, I’d agree with David that it’s not an ideal solution - another point of failure, something that’s easy to get wrong or to have fall over. Having your blog inaccessible for a period when a crawler arrives is certainly not going to help with any SEO!
I think there may be another option though - but I’m not 100% sure so perhaps @DavidDennison or @Sam62 would advise on this one. My SEO skills are not really that up-to-date 
What if you 301 redirected from your external non-HS website (www.mysite.com/blog/my-article) to the HS blog (blog.mysite.com/my-article). Depending on how that external site is hosted, it could be a fairly simple wildcard redirect, i.e. tell it to redirect /blog/* to blog.mysite.com/*.
Or is there no actual benefit to doing that?
Cheers,
Mike