I'm new to the board, but have been in the paper industry for over 20 years. Thought you may be interested in some paper tidbits as you select paper for PP bullets.
The reason some paper doesn't wrap well/or get wet well is due to the fact they are "sized." Sizing is an additive added to either the wet end or the dry end (size press) of a paper machine. Sizing agents are designed to provide water hold out of aqueous inks-which produces a sharp printed image or sharp lettering. Sizing agents can be (for alkaline paper): ASA, AKD in the wet end, or various styrene acrylics in the size press. It doesn't make paper "water proof" just "resistant to water." They is a test called the "HST" or "Hercules size test" which (simplified) is a special ink added to one side of the paper. A sensor is on the other side of the sheet, and when the ink shows up on the sensor side, the test is done. The degree of sizing is recorded in seconds. So a heavily sized sheet will have a longer time than a low sized (slack sized) sheet. You can do a quick test by licking the paper and seeing if the water bleeds through the paper at a certain time (ie 5 seconds, 10, 20 100, 500 seconds etc).
Newsprint is not sized. You lick it, and water bleeds through immediately. by contrast, bond type of paper has medium to high sizing (pending the grade). The lower the basis weight of the paper, the more important sizing is. You have a thinner sheet, which has to hold out water. You don't have the mechanical barrier of thick fiber. For "onionskin" paper, sizing is pretty high.
So you have a problem. Low basis weight (bw) to wrap bullets, but high sizing for poor "wetting" ( the opposite of sizing). It will wet, it just needs more time.
Another issue to be concerned about, but you never read about it is the issue of abrasiveness of paper. Paper has various levels of inorganic filler. It is added to provide opacity and sometimes brightness qualities to paper. Paper is made by two processes, acid or alkaline papermaking. Most paper is made by alkaline systems. It has more "permanence" meaning it will last longer. Old books in libraries have pages that are brittle and crack. This is acid made paper. (low permanence). Anyway, the filler used in acid paper is typically clay. The filler used in alkaline paper is typically calcium carbonate (CaCO3). It's also called "pcc" (precipitated calcium carbonate). Ok, there is also "Gcc" for "ground CC" but they are all inorganic fillers. Lighter basis weight paper needs opacity, and ofter titanium dioxide ("tiO2") is used to provide extra opacity (good paint has higher levels of tiO2 for it's "hiding" effect for improved opacity.).
Filler levels ("ash content") various from low to high, but can be easily 20-25%+ of the total weight of paper. PCC is cheaper than fiber, so a papermaker wants to add as much pcc as possible. It also weakens the sheet, so then you have to make other changes in the fiber furnish permit the machine to run at high speeds ( ie adding starch, or increased kraft).
Ash is abrasive. You want a sheet that has low ash so your bores don't wear out. How long with barrels last? Don't know for sure, as most people don't shoot that much, but it is a factor. Paper machines have equipment wear out due to the pcc abrasiveness. Rifle barrels aren't that different.
So what does all this "papermaking 101" lesson mean? You want a thin sheet with low ash, and low sizing. This my friends, is NOT writing paper. This screams to me as "LENS PAPER." Find some good lens paper, and youo will have some slick paper to wrap those chunks of lead. lens paper doesn't have filler, as they realize that it will be abrasive to lens coatings and lenses. It's strong, and its lightweight (thin).
Hope this helps.