Yes, rechambering a 44 Mag Handi to a 445 Super Mag chamber without a lathe is very doable. Note that the Super Mag probably operates at a higher presure than the Mag does, adding case volume alone rarely increases velocity by as much as 20%, which is what some 445 Super loads are doing. this is ok, H&R once chambered thHandi in 444 Marlin, and the 44 Mag has a case diameter very similar to the 30-06/308 family. Presure is not a problem. But also note that there is nothing in a Handi that the 445 Super Mag offers that cannot be achieved with the 444 Marlin and starting loads for the same, and brass is much cheaper. Starline is the only supplier of 445 brass and it starts at $32.00 for 50. A bit pricey for what could be considered 44 Mag basic brass.
My solution to more big bore performance from a Handi was to simply get a 45-70 Handi. This chambering is capable of giving 44 Magnum heavy bullet performance(300 grain at 1200 fps and better), 454 Casuell and 475 Linebaugh performance (400 grain at 1400 fps and better), and 45-110 performance (500 grain at 1600 fps). I looked at different chamberings, paper stats, etc. for a year, and finally decided on the 45-70 simply because there is more component availability and cost effectiveness than with any other big bore chambering that can be readily stuffed into a Handi out there. Your choice, but I would not choose a 445 Super Mag. over a 45-70. The latter just simply offers too much potential at half or less the cost. The 44 mag Handi remains a great rifle with a definte niche, but a rechambering to the 445 SM would be a step backwards.