I'd cut my inventory to nothing (including armor), open the old game, copy the inventory (under player) then open the original and replace the entire inventory (delete), you can also delete/rename inventory1 to inventory.
It is possible to add one item but I have trouble every time I try. I often get a conflict and overwrite someting I want in the csane slot.
CLOSE ALL MineCraft games before using NBT and remember to save all changes.
I suggest you make a copy of your current game to the desktop or somewhere else for insurance, first.
Your inventory is stored within level.dat, although if you just copy it over it will reset everything else in your inventory, Ender chests, and any mod data that is stored within it (it sounds like you are using mods).
It is possible to use a tool like NBTExplorer to copy over a single item though; player data is stored under the "player" tag, which in turn stores your inventory under "inventory", which is a list of tags containing the item ID and other data; the item name itself will be the internal name, such as minecraft:diamond_pickaxe, or just diamond_pickaxe (or the name of a mod and its item if it was a mod item; if you are in 1.7.10 or earlier it will a number, such as 278, the numerical ID for a diamond pickaxe). There are also tags for a custom name (if renamed) and enchantments, which can be used to figure out which is the right one if you had more than one. If you do this, make sure that the slot it was in is empty in the current save, or change the slot number to an empty slot (and as always, make a backup before doing this).
Alternatively, you could open to LAN and enable cheats and give yourself a new pickaxe without having to mess around with the save files (note that cheats will be disabled when you reload the world).
You don't need any fancy tools, this is supported by default these days. But you'll need creative mode.
Once you have the item in one of your hotbar slots just save the current hotbar. Default key combination is x + number. You got 9 hotbars which you can save. So if you want to save to the first slot just press: c-1. Press and keep the c key pressed, then press 1. After that your toolbar is saved and you can retrieve it everywhere you got creative mode. Whether it's a different save game or even an online server. As long as you have creative.
To retrieve these items just press x + number. So if you followed up on my example of using the first slot then you'd now press x-1 and you'll have your item again.