Okay, so on the urination mod: 1/4" drill bit does the job on the cover.
Important: To remove the nozzle, just grip it with pliers and pull. Be gentle to avoid damaging it; I recommend using a piece of rubber to protect it if possible.
As for dremels: Cheap ones can be had for $20 or less at discount stores and Harbor Freight. If you're getting a cheap one, do NOT get a DC (9v, 12v, cordless, etc) powered one; get AC powered only. If you're willing to drop >$50 then a cordless one might be ok. The cheap DC powered ones have NO torque, and even my $80 (a few years ago) Craftsman cordless one is too wimpy at times, forcing me to get an extension cord and use my $10 AC powered one.
http://www.harborfreight.com/cpi/ctaf/displayitem.taf?Itemnumber=40457
Ok, that's $24 right now, but they are constantly moving their prices around, one week this is on sale, next week that is.
When you buy one, I highly recommend a diamond cutoff blade. They're far more useful than the normal abrasive cutoff blades that break when you try to use them. The diamond ones can also be used for sanding/smoothing with their surface, not just cutting with their edge.