Mesh on Walking shoes

Unless your boots have a Gore-tex liner or similar a mesh or woven upper will not be "waterproof". That said, you can improve its water shedding properties with surface treatments like the appropriate Nikwax product:
http://www.nikwax.com/en-us/productselector/productselector.php
ie. Nickwax "Fabric and Leather"

Nikwax Fabric & Leather Proof™ is easy and quick to apply; either
spray or sponge on to wet shoes. Nikwax Fabric & Leather Proof™
provides highly Durable Water Repellency (DWR) which develops on air
drying. It leaves a flexible water repellent treatment on individual
fibres of fabric and leather. This allows moisture vapour to pass
through, maintaining breathability and keeping your feet dry. Nikwax
Fabric & Leather Proof™ has been specifically designed and optimized
for fabric and leather combination footwear.

For walking about in a urban environment, you really don't need the same level of "waterproofing" as walkabouts in the bush. Just try to not step in puddles or on Paris urban landmines.

All of what Edgar quoted is marketing hype. I have never found any after market product that is truly waterproofing or even water resistant for any period of time. The surface treatment may be good or an hour or so and may require re-treated to maintain even a bit of water resistance. The weakness to any surface treatment is the stitching. Nearly impossible to waterproof holes. If waterproofing is need then you need to take waterproof shoes or something that is certified waterproof. There is one little trick you can use. Take along on large plastic bags (depending on foot size maybe gallon or quart zip lock bags) and slips those on between your sock and the shoe. The shoe will get wet but the foot stays dry. Good luck.

http://www.rei.com/learn/expert-advice/caring-hiking-boots.html

When Hiking Boots Are New: New hiking boots rarely require treatment
out of the box. Reason: Nearly all boots are factory-treated with a
durable water repellent (DWR) finish.

After Extended Use: Clean, Condition, Waterproof: Use a cleaner when
preparing to apply waterproofing, or any time stubborn residue (dust,
mud, grime) is visible on the upper.... Use a conditioner when
full-grain leather boots appear dry or cracked. ... Use a
waterproofing treatment when water does not speedily bead up and roll
off a boot's surface, allowing water to sink into the exterior
layer....

Q: When the DWR finish on boots needs to be restored, what
waterproofing product should I apply?

A: Your decision depends on the material used in the uppers of your
boots and what brand appeals to you.

Material: Some brands make specific products for particular boot
materials: Full-grain leather Split leather (aka reversed or
roughed-out leather) Nubuck Suede Synthetic leather or a fabric and
leather combo Brands: REI carries waterproofing products from Nikwax,
Granger's and Tectron. (Note: REI's product assortment changes
intermittently. Nikwax is the most prominent brand, endorsed by Asolo,
Burton, Merrell, Nike, Raichle, Salomon, Scarpa and other
footwear-makers. U.K.-based Granger's products also have a strong
following.

How about wear the wp boots when it's wet/rainy and save the Merrill's for the (hopefully) sunny/dry days?

Continuing to quote marketing materials doesn't prove any of that stuff works beyond a short period of time. I have a pair of ECCO shoes that were designed to be waterproof and ten years later they still are despite being soaked a half dozen times. Never had to apply any treatment. The point is - it is extremely difficult if not impossible to make a shoe waterproof with after market applications. If a waterproof shoe is needed, then get a waterproof shoe.

jsdsnv, what is it that you are anticipating to encounter for which you need two pairs of waterproof shoes? Waterproof to me means a pair of galoshes.

Thanks for all of the advice! I want to have these shoes just in case and certainly only wear them when the weather suits them.

I am just petrified of getting blisters so want these with me. I love the bag idea!

Take some moleskin with you - I've never used it but know people who have and it is great help if you end up with a blister...