Want ghetto-tech? I'm your huckleberry. Check it:
* Cigar box (available at a cigar store [I derp in jest
] big enough to fit the pipe laying down; something with a closing hasp to stay shut)
* A piece of white styrofoam (insulation panels at the hardware store; be sure they're a thickness to fit in the cigar box)
* A piece of velveteen from the fabric shop (enough to wrap the foam brick that'll fit in the box).
* Paint (something with a flat finish).
* Glue (something that won't melt foam, good ol' wood glue works).
Cut foam into a brick that will fit not-quite-snugly into the cigar box. Sharp kitchen knives work great. Take said pipe, orient it in the center of foam brick. Press the pipe firmly so the foam makes an indentation (this will be the pattern). Using something sharp, cut into the indentation carefully about 3/4 the width of the pipe. You should end up with a pipe-shaped trough that...well... fits the pipe. Not too tight, not too loose.
Cut a piece of velveteen enough so you can press it into the foam pipe trough, and around all the edges. Wrap foam block to measure. Once you are comfortable with the fit, put four glue spots, one in each corner on the same side of the foam block as the pipe trough you carved. Make sure there's enough slack for the pipe to recess into the foam and stay there. Let glue dry. Once dry, wrap the flaps of velveteen over the foam and on the opposite side of the pipe trough, and glue them in place. As a tip, you might have to cut some material and get the right "fold" to make it sit right so it doesn't look like poo.
Paint your cigar box, being careful not to paint over the nice metal hardware (if any). If there were embossed logos in the wood, sanding them first helps make a better-looking finished product.
The inside of the lid will be another matter, which might have a gap of varying degree. What I'd suggest is painting the inside (sanding too, if applicable) and cutting a little foam spacer to go directly in the center, also covered with a little velveteen. This will help keep the pipe from knocking around inside the box as it is closed.
There's your idea. Adjust accordingly.