Hi @Fursty,
This really depends on what you mean by "shift". Let me try to explain what Canvas CAN do with html tables...
If you want to add a row or column (essentially what I'd call shifting all rows/columns down/right), Canvas can do that. You'd put your cursor in the first cell you want to shift, then use the icons at the bottom of the table. In this example, my cursor was in r2c1 and I clicked the insert row above button...
Now if you want to only affect certain rows or columns, you can highlight the cells you want to move by click+drag, then use cut (cmd/ctrl+x) then move the cursor to the upper-left cell you want those cells to start in again and paste (ctrl/cmd+v). In this example, I highlighted the cells shown, then pasted them with my cursor in r3c2. This essentially shifted the highlighted cells one column to the right. With this tactic, you do need to have enough empty space for the content to be pasted, otherwise it would overwrite existing content
I hope this info helps!
-Chris