How Is Intensity of Blue Light Measured?
I feel for you.  Been there done that.  I design LED grow lights for Horticulture Research at the University of Florida. 

LEDs are so much more complex than one would think.  So much so I am currently writing a paper titled "Understanding LEDs"

There are blue LEDs and there are Royal Blue LEDs.
Blue is typically around 475nm
Royal Blue is typically around 450nm

The bandwidth of a Royal Blue stretches out to around 400nm near UVA and hitting the limit of human advisably (about 400nm).  Blue does get as close so it is still considered Luminous.   

Blue is visible so measured in Luminous units typically lumens.
Some of Royal Blue wavelength spectrum is not really visible.  The eye can react to 400nm but it is perceived so much less by the eye Royal Blue is almost always measured in Radiant Units mWatts of flux. 

I have seen studies on the photoreceptors in the retinal ganglion cells with a highest sensitivity of 470-490 nm blue light on the effects of short-wavelength light in humans. Several studies have explored the efficacy of monochromatic blue or blue-enriched light in the treatment of syndromal seasonal affective disorder(SAD) and Sub-SAD.

One study,  The effects of low-intensity narrow-band blue-light treatment compared to bright white-light treatment in sub-syndromal seasonal affective disorder used a 470 nm, Philips, goLITE HF3320. So we are probably talking Blue not Royal Blue.

To answer your question on comparing mWatts to Lumens it can be estimated. 

The perceived brightness, or luminous efficacy, of light is technically specified by the International Commission on Illumination (CIE).  Each wavelength efficacy is  related to a wavelength of 555nm (Lime Green).

I am only somewhat confident these number are relevant.  I do need to have someone else verify they are correct before I publish. 

I created this table for common LED colors

What I am going for here is the factor to convert mWatts to Lumens.  To convert other colors to the 555nm equivalent output flux, multiply the LED's published lumens by the reciprocal of the CIE factor.

CIE sets the spectral luminous efficacy of the human eye for each wavelength starting a 555nm.  The CIE defines photopic vision as 683 lumens/watt at 555 nm.  

This I wrote a PHP script to create an SVG image from the table of CIE  table of CIE Photopic Luminous Efficacy.

Royal Blue wavelength is 450 where the CIE luminous efficacy is 0.038.  

Using the  CIE photopic luminous efficacy for 450nm of 0.038 we can convert lumens to the approximate Radiant flux (mWatts):

(lumens÷683) / 0.038 = mWatts


Conversely 

mWatts ×  0.038 × 683 = lumens


BOTTOM LINE

None of this should matter. If you are using Blue (470nm) and not Royal Blue(450nm).  Blue is almost always specified in lumens.  You should be able to ignore any measured in mWatt. 

WHAT YOU WANT

You probably want either Cree XPE or Lumiled Rebel ES Color LEDs.  Which depends on what is available at the time you order them.

Cree
Lumiled

You probably want the ones circled in Red.  But you are going to need between 6 and 8 each to reach 250 lumens.

Notice the blue circle on the Lumiled Blue.  This is another thing you have to watch out for when comparing LEDs.  LEDs are spec'ed out at various currents.  The one circled is pumping twice the current of all the others. 

Temperature affects luminous flux significantly. Some are spec'ed at 25º C others 85º C.