If you want to measure with a µCurrent:
You can still use your PicoScope to do the measuring by putting the µCurrent in place of the resistor that you've been using as a measurement shunt.
3.5µA is higher than what the µCurrent's nA range can measure, so you would have to use the µA range. 3.5µA is a pretty low value for the µA range, so your readings in that region won't be too accurate, but you'll have to live with that.
When the current jumps to the "around 15mA" that you stated, or actually anything over about 1.2mA, the µCurrent will pin at around 1.2V output (looking like 1.2mA) so you won't be able to measure these high currents while on the µA range. However, I've made estimates that say that the µCurrent should safely be able to handle 28mA on the µA range, at all times, and up to 85mA while powered on, so your 15mA shouldn't do any damage to the µCurrent.
So, you'll first have to integrate the readings on your scope that are below the 1200µA limit, using the µCurrent's µA range, then switch to the mA range and integrate the areas that are above 1200µA. Adding the two integrations should allow you to calculate the average current. 15mA is a small percentage of the full scale mA range, so accuracy will again suffer, but that's a limitation of the µCurrent's available ranges.
Here's a video that Dave did about using integration with an oscilloscope:
http://youtu.be/Dh0xYu8YvaEMy calculations for maximum safe currents for the µCurrent can be found in the following post and the one that is referenced in it:
https://www.eevblog.com/forum/crowd-funded-projects/current-gold-on-kickstarter/msg376311/#msg376311If you're interested in adding protection so that the µCurrent can safely handle higher currents when powered off, you can look at this post about the mods that I've made to mine:
https://www.eevblog.com/forum/crowd-funded-projects/current-gold-on-kickstarter/msg448208/#msg448208