The simplest thing is to make a small Word document, just containing the symbols you want to use regularly, keep it open in a little window which you can copy from to paste into your document. You could make simple macros for each symbol to copy them to the clipboard.
If you have just a few symbols (like half a dozen) in common use in your work, you could decide on which characters in your usual font that you don't use* on your keyboard, and edit your commonly used font so that when you press the key for say ~, ° is displayed instead. All that you need do is copy your required glyph to the position in the font occupied by the glyph that you never use. When you make a change to a font file, save it with a different font name, and embed it in your document.
* like these perhaps: `¬ |~#}{[]
Most fonts are copyrighted. I don't know if just changing the position of a glyph in a font has any copyright implications. It certainly makes no visible difference to the document. Remember, some fonts come in families, with bold and italic versions too. If a font is embedded in a document it becomes transportable. If just for local printing, it need not be embedded.
If you google "free font editors" or "glyph editors" you may find an editor that you like.
In Windows there is the Private Character Editor,
eudcedit.exe , which almost nobody knows about, and
Charmap.exe which few people use, as far as I know, but lets you discover and use the range of symbols hidden in the fonts. The newer SegoeUI font family has an amazing set of symbols related to the Windows User Interface, which has evolved over the last few generations of Windows since Vista.
Microsoft have a section of their website dedicated to typography:
Microsoft Typography - Free font information, TrueType, OpenType, ClearType containing free tools, articles and links.
